Preheat oven to 350°F (175°C).
In a bowl, whisk together flour, baking soda, salt, cinnamon, ginger, and nutmeg.
In another bowl, cream butter and brown sugar until fluffy.
Add egg and vanilla extract to the creamed mixture and mix well.
Gradually add dry ingredients to wet ingredients and mix until a soft dough forms.
Roll dough into small balls, about 1 tablespoon each, and place them on a lined baking sheet.
Press a small indentation into the center of each dough ball using your thumb or a spoon.
Fill each indentation with a small spoonful of strawberry jam.
Bake for 12 to 15 minutes until the edges are lightly golden.
Allow the cookies to cool completely on a wire rack.
Mix powdered sugar, softened butter, milk, and vanilla extract until smooth and pipeable.
Transfer the frosting to a piping bag and pipe a swirl around the jam center on each cookie.
Let the frosting set slightly before serving.