Preheat your oven to 350°F and line two baking sheets with parchment paper. Combine flour, 1 cup sugar, baking powder, and salt in a large bowl and whisk it together. In another bowl, beat softened butter with eggs and vanilla until you get a fluffy, light mixture.
Stir the wet ingredients into the dry ones until everything comes together into a soft dough. The texture should feel kinda like play-dough—soft but not sticky. If it feels too wet, add 1 tablespoon more flour and mix again.
Make the filling by beating softened cream cheese until it's smooth and creamy. Add strawberry jam and chopped fresh strawberries, then sprinkle the cornstarch on top and fold everything together gently. The cornstarch keeps these strawberry cheesecake stuffed cookies cozy from getting that watery filling issue.
Scoop out 24 cookies using a 1-tablespoon cookie scoop or small spoon. Press your thumb into the center of each cookie to make a little pocket for the filling.
Spoon about 1/2 teaspoon of the strawberry cream cheese filling into each cookie pocket. Don't overstuff because the filling expands while baking and you want to avoid leaks (yes, I learned this too).
Bake for 12 minutes or until the edges turn golden brown but the centers still look a little soft—don't panic if they look slightly underdone because they keep cooking after you pull them out. Let them cool on the baking sheet for 3-4 minutes before transferring to a wire rack.
The cookies will firm up as they cool completely. Eat them warm, serve them at room temperature, or store them in an airtight container for later.