Prepare the Tart Dough: In a bowl, mix flour, sugar, and cold butter, rubbing together until it resembles coarse crumbs. Add cold water and mix until a dough forms.
Chill & Roll: Wrap the dough in plastic wrap and chill for 30 minutes. Roll out on a floured surface and press into a tart pan. Prick with a fork and pre-bake at 180°C (350°F) for 10 minutes.
Make the Almond Filling: In a bowl, whisk together ground almonds, sugar, eggs, cardamom, melted butter, and vanilla extract until smooth.
Assemble & Bake: Pour the filling into the pre-baked tart shell, sprinkle with sliced almonds, and bake at 180°C (350°F) for 25 minutes, until golden and set.
Cool & Serve: Let the tart cool before dusting with powdered sugar. Serve with whipped cream or a cup of coffee.