Mix together dried strawberries, 1 cup water, granulated sugar, 1 tablespoon lime juice, and lime zest in a medium saucepan over medium-high heat. Stir mixture constantly and bring to a boil. Reduce heat to a simmer, stirring occasionally, until mixture is thick and most of liquid has been evaporated, about 15-20 minutes. Remove from heat and stir in 1 teaspoon rum extract.
Meanwhile, in a small bowl toss together fresh strawberries and cornstarch until well combined. Add to pan with dried strawberry mixture, and stir to combine. Set aside to cool completely.
Unroll pie dough onto lightly floured surface (or on parchment paper or silpats). Using a 3-inch round cookie or biscuit cutter, cut-out dough to form 48 rounds. Roll out scraps as necessary to get more rounds if necessary.
Press the end of a lollipop stick into the bottom 1 to 1 1/2 inch of each dough round.
Whisk together egg and 1 tablespoon water in small bowl until well combined. Brush dough rounds with the lollipop sticks with egg wash.. Place about 1 tablespoon of strawberry mixture over lollipop sticks in middle of dough rounds.
Cover dough rounds with strawberry filling with remaining dough rounds pressing firmly around edges to seal. Crimp edges with fork. Brush top of each round with egg wash.
Place pie pops on parchment (or silpat) lined baking sheets and freeze about 30 minutes. Meanwhile, heat oven to 375 degrees F.
Remove pie pops from freezer and poke several holes in each top crust with tip of sharp knife. Bake at 375 degrees F for about 22-27 minutes, rotating pans halfway through baking, until tops are golden brown. Cool slightly.
In small bowl, mix together powdered sugar, 1/2 teaspoon rum extract, and 1 tablespoon lime juice. Add more lime juice as needed to form glaze. Drizzle or spread glaze over pie pops.
SNAPPY TIPS: After pie pops have been frozen for 30 minutes they can be stored in an airtight container or resealable bag in the freezer for up to a month. Bake as directed.SNAPPY SUBSTITUTIONS: Instead of rum extract you can substitute vanilla. Instead of lime zest/juice you can substitute orange zest/juice.