In a large mixing bowl, whisk together flour and confectioners' sugar until well combined. Cut in cold butter until the mixture resembles coarse crumbs. Shape the dough into a ball, cover with plastic wrap, and chill for 30 minutes.

Preheat your oven to 350°F (175°C). Remove the dough and roll it into twenty-four 1-inch balls. Grease muffin cups, and press each dough ball into the bottom and sides to form small tart shells.

In another bowl, beat together almond paste and softened butter until creamy. Add egg white and almond extract, mixing until fully incorporated.

Spoon approximately 2 teaspoons of almond filling into each tart shell, ensuring a slight dome shape.

Bake the tartlets for about 20-25 minutes, or until golden brown around the edges. The filling should be set.

Cool tartlets in the tin for 5 minutes, then transfer to a wire rack. Top with apricot preserves for a glossy finish.

Arrange on a platter, optionally dusting with confectioners' sugar. Serve warm or at room temperature.