Preheat the oven to 350˚F and line 2 baking sheets with parchment paper.
Whisk together the flour, baking powder, and salt in a large bowl.
Beat together the butter and sugar in a stand mixer fitted with the paddle attachment on medium-high speed until light and fluffy, 2 to 3 minutes.
Add the eggs, one at a time, followed by the vanilla.
Reduce the mixer speed to low and beat in the flour mixture until just combined.
Using a rubber spatula, fold in the freeze-dried strawberries and white chocolate chips.
Scoop the batter into roughly 2-tablespoon-size balls.
Roll between your hands until smooth, then arrange 2 inches apart on the prepared baking sheets.
Bake until golden brown, 10 to 12 minutes, rotating the pans halfway through.
Let cool for 5 minutes on the baking sheets, then remove the cookies to a rack to cool completely.
Transfer half the cookies to a separate baking sheet and flip them upside down.
Top each with a scoop of ice cream (about ⅓ cup), pressing down lightly with the back of the scoop to flatten.
Place another cookie on top of each, then freeze until solid, about 3 hours.
The ice cream sandwiches will keep in the freezer, wrapped in plastic wrap, for up to 1 month.