Preheat oven to 350ºF. Lightly butter the bottom and sides of a half sheet pan (18-by-13-inches); line with parchment paper, leaving at least an inch of overhang on the two long sides.
In bowl, whisk together flour, milk powder, baking powder, and salt and set aside.
In saucepan set over low heat, melt butter until it starts to foam and bubble. Add granulated sugar and stir until sugar is somewhat dissolved. Remove from heat and add white chocolate; let sit for 30 seconds then stir until fully melted. Continue mixing vigorously until mixture is homogenous and no longer has a slick of butter floating on top (it will look sort of like sweetened condensed milk).
Meanwhile, in the bowl of a stand mixer fitted with the whisk attachment, beat eggs, brown sugar, and vanilla on medium-high speed for 2 to 3 minutes or until thickened and lightened to the color of peanut butter.
With the mixer running on low, drizzle in melted white chocolate mixture and mix until just incorporated, scraping down the sides of the bowl with a spatula as needed. Sprinkle dry ingredients over top and mix on low speed or fold in with a spatula until just incorporated.
Pour batter onto prepared baking sheet, and spread into an even layer using an offset spatula. Sprinkle evenly with chopped pistachios.
Bake for 13 to 15 minutes or until top is crackly and edges are golden brown. Place sheet pan on a wire rack to cool completely, then refrigerate or freeze for at least 30 minutes (or more) to make it easier to work with (you can make it ahead of time and refrigerate/freeze overnight too).
While the blondie is chilling, prepare an 8-by-8-inch square baking pan (ideally one with crisp, sharp corners and straight rather than angled sides). Line the bottom and sides with two 8-inch-wide by at least 14-inch long strips of parchment paper placed perpendicular in the baking pan, creasing the corners and top edges. You should have a good inch or two of overhang; you will need this later to lift the sandwiches out of the pan.
Carefully lift and slide the chilled blondie onto a large cutting board, leaving the parchment on the bottom. Use a ruler to measure and cut two 8-inch squares (should be exactly the same size as the inside of your baking pan). Use a large knife or a sharp rotary cutter to cut through the blondie and the parchment lining the bottom.
Gently lower one of the squares into the bottom of the parchment-lined baking pan, pistachio side down, then peel off parchment backing. Put the pan and the other square back in the fridge or freezer until the ice cream is ready.
To make the ice cream: combine sweetened condensed milk, pistachio butter, pistachio extract, and salt in a large mixing bowl. Add a few drops of green food coloring if desired.
Pour the cream into a clean (and preferrably chilled) metal mixing bowl or the bowl of a stand mixer fitted with the whisk attachment. Sift powdered sugar over top, then turn mixer to medium-high speed and whip until cream forms medium peaks (try not to overmix or it will be harder to incorporate).
Spoon in about 1/3 of the whipped cream into bowl with pistachio mixture, folding and gently stirring to lighten up the mixture. Add remaining whipped cream and fold with a large rubber spatula until evenly incorporated and no streaks of bright white cream are visible.
Pour ice cream base into square pan, spreading into an even layer. Gently peel off the parchment and place the second blondie square, chopped pistachio side up, on top of ice cream, pressing lightly to adhere (don't press too hard or the ice cream may squeeze out the sides; you can also freeze the ice cream for 30 to 45 minutes to let it set up a bit before adding the top layer of blondie).
Lay one of the leftover parchment squares on top of the pan to keep out any undesirable freezer flavors; place pan somewhere level in your freezer and freeze until completely set, at least 4 hours or overnight.
Before serving, use the parchment paper overhang to lift the entire block out of the baking pan and onto a cutting board. Use a large knife (running it briefly under hot water to make it easier) to cut sandwiches into 16 even squares. Wipe or rinse off the knife between each slice for the cleanest looking cuts. Serve immediately, or return cut squares to the freezer to enjoy later (if storing longer than a day, put them in an airtight container or wrap individually with plastic wrap). Sandwiches will keep for up to 2 months.