Preheat oven to 350°F. Grease a 9-inch tart pan with butter and set aside.

In a large mixing bowl, combine flour, brown sugar, cinnamon, nutmeg, and ginger. Mix well to distribute spices evenly.

Add melted butter to the flour mixture and stir until the mixture resembles coarse crumbs and holds together when pressed.

Press the cookie mixture firmly into the bottom and up the sides of the prepared tart pan, creating an even layer.

Bake the crust for 12-15 minutes until lightly golden and fragrant. Remove from oven and let cool completely.

While crust cools, prepare the filling. In a medium saucepan, heat milk and heavy cream over medium heat until just simmering.

In a separate bowl, whisk together eggs, sugar, vanilla extract, and a pinch of cinnamon until smooth.

Slowly pour the hot milk mixture into the egg mixture while whisking constantly to temper the eggs.

Return the combined mixture to the saucepan and cook over medium-low heat, stirring constantly, until thickened enough to coat the back of a spoon, about 8-10 minutes.

Remove from heat and stir in butter until completely melted and incorporated. Strain the custard through a fine-mesh sieve into a clean bowl.

Pour the warm custard filling into the cooled tart shell, spreading evenly. Refrigerate for at least 3 hours or until completely set.

Before serving, crush remaining speculoos cookies into coarse crumbs. In a small skillet, melt butter and add cookie crumbs, stirring until lightly caramelized.

Sprinkle the caramelized cookie crumbs over the top of the chilled tart just before serving. Cut into slices and serve cold.