Preheat oven to 350°F and line large rimmed baking sheets with parchment paper.
In a large microwave-safe bowl, melt butter in 20-second bursts, then stir in peanut butter until smooth.
Add light brown sugar and granulated sugar to the butter mixture and whisk together, then set aside to cool until just warm.
In a medium bowl, whisk together the flour, baking soda, baking powder, and salt.
Add eggs, milk, and vanilla to the butter mixture and whisk until fully combined.
Fold in the flour mixture with a sturdy spatula until just combined.
Use a large spring-loaded cookie scoop (3 tablespoons) to portion dough, then roll into smooth balls.
Create a thumb well in each dough ball, fill with 1 heaping teaspoon of chilled strawberry jam, then partially seal and roll back lightly to allow jam to peek through.
Place dough balls on baking sheet spaced 3 inches apart with jam side up.
Bake for 14 minutes or until puffed and edges are lightly browned.
Cool cookies on baking sheet for 5 minutes then transfer to a wire rack to cool completely.
Store in an airtight container for up to two days; cookies soften over time.