In another bowl, beat butter and 1 1/4 cups sugar until light and fluffy (about 2-3 minutes on medium speed), scraping the bowl as needed.

Mix in the egg, followed by vanilla extract and food coloring.

Gradually incorporate the dry ingredients, then blend in 1/4 cup strawberry jam until fully combined—no visible streaks should remain.
Divide dough into 12 portions, rolling each into a ball. Coat with the remaining 3 tbsp sugar and press an indentation into the center of each.
Arrange on a parchment-lined baking sheet and chill in the refrigerator for 2 1/2 hours.
Preheat oven to 325°F (163°C) and line two large baking sheets with parchment.
Transfer chilled dough balls onto the baking sheets, spacing them 3 to 4 inches apart.
Fill indentations with remaining jam and bake for 15 minutes, until edges turn slightly golden while tops remain pale. Cool completely.
Preparing the Glaze & Finishing the Cookies
While cookies cool, whisk together powdered sugar, jam, water, and food coloring until smooth.
Drizzle the glaze over cooled cookies.
Let set, then enjoy your jam-packed strawberry delight!