Mix cold cream cheese, 1/4 cup of granulated sugar, and 1/2 teaspoon of vanilla extract in a medium bowl using an electric mixer on medium speed until fluffy and smooth, about 2-3 minutes. Scoop into dollops on a parchment-lined baking sheet and freeze for 30 minutes.

In a saucepan, combine 12 ounces of finely diced strawberries with 3 tablespoons of sugar. Cook over medium heat while stirring until thickened, about 40-45 minutes. Cool completely after thickening.

Preheat oven to 350°F (175°C) and line a baking sheet with parchment. In a large bowl, whisk together flour, baking powder, baking soda, and salt. In another bowl, cream butter and sugar until fluffy. Add egg and mix until incorporated.

Gradually mix dry ingredients into wet mixture until just combined. Fold in cooled strawberry jam gently to keep pockets of flavor.

Using a cookie scoop, form cookies around a frozen cheesecake dollop, ensuring it's completely encased. Repeat until all dough is used.

Roll each cookie in extra sugar before placing on the baking sheet. Bake for 11-12 minutes until edges are golden brown and centers remain soft.

Let cookies cool on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely.