Prepare the cream cheese filling: Beat cream cheese, powdered sugar, and vanilla extract until completely smooth. Drop 1-2 teaspoon dollops onto parchment-lined tray. Freeze for 30-60 minutes until rock-hard.
In a stand mixer or with hand mixer, cream butter with brown sugar and granulated sugar on medium-high speed for about 3 minutes until light and fluffy.
Add egg, vanilla extract, strawberry extract, and food coloring (if using). Mix until fully combined and dough has uniform pink color.
In separate bowl, whisk together flour, baking soda, baking powder, and salt. Gradually add to wet mixture on low speed, mixing until just combined. Dough should be thick and slightly tacky but not sticky.
If dough is too sticky, add flour 1 tablespoon at a time until workable. If kitchen is warm, chill dough for 20 minutes before stuffing.
Take about 2 tablespoons dough and flatten in your palm into a disc. Place one frozen cream cheese dollop in center. Fold dough around filling, pinching edges to seal completely with no cracks or gaps.
Roll stuffed ball between palms to create smooth surface, sealing any visible seams. Roll ball in granulated sugar to coat completely.
Place sugar-coated cookies on parchment-lined baking sheets, spacing at least 2 inches apart. Repeat with remaining dough and filling.
Preheat oven to 350°F. Bake for 10-12 minutes until edges are set and slightly golden while centers remain soft. Cookies may look slightly underdone.
Let cookies cool completely on baking sheet. This allows filling to firm up and prevents cookies from breaking. Do not move them while hot.