Preheat oven to 350°F and line two baking sheets with parchment paper or spray with cooking spray.
Make the crumble topping: In a medium bowl, whisk together the flour, brown sugar, oats, cinnamon, nutmeg, ginger, and salt. Add in the cold, cubed butter. Using a pastry cutter or your hands, work the mixture together until all of the ingredients are combined and it’s crumbly. Set side.
In a stand mixer with paddle attachment (or with a hand mixer), beat the butter and sugar until light and fluffy, about 3-4 minutes. Add in the vanilla and milk and mix until combined.
Reduce the speed to low and gradually add the flour and salt. Mix only until the point that the dough starts to come together. It will appear crumbly but, if you squeeze a handful, it should hold together.
For each cookie, scoop about 1/4 cup of dough into your hands and give it a gentle squeeze so it comes together. Roll to form a ball, then gently press it down to form a circle. Press your thumb into the center of the dough creating a little indentation and place it on the lined baking sheet. Leave a little space between cookies (but they won't expand too much).
Spoon a teaspoon of jam into each cookie indentation.
Sprinkle the crumble topping evenly over the tops of each cookie.
Bake for 17-19 minutes, until lightly golden around the edges.
Let cool for at least 10 minutes before enjoying.