Preheat oven to 375°. Whirl almonds in a food processor until finely ground. Add flour, baking powder, and salt and whirl to blend.
In a large bowl, beat butter, 1 cup granulated sugar, the vanilla, and almond extract with a mixer until creamy. Add eggs one at a time and beat until well blended, then beat in milk (batter will look curdled). Stir in flour mixture until smooth.
Butter bottom and sides of a 12- to 13-in. tart pan with a removable rim. Spread batter level in pan. Randomly arrange fruit slices on their wide sides about 1/2 in. apart on batter and press into place. Sprinkle all over with remaining 2 tbsp. granulated sugar.
Bake until a toothpick inserted into center of cake (not in fruit) comes out clean, 35 to 40 minutes. Let cool on a rack. Loosen cake from rim with a knife and remove rim. Sift a light coating of powdered sugar on top and cut into wedges.
*Toast almonds in a 350° oven until golden, 8 to 10 minutes. Let cool before grinding.