These tartlets get a double dose of nutty goodness from toasted almond flour and browned butter.
Preheat oven to 425 degrees. Melt butter in a small saucepan over medium heat. Cook until butter turns golden brown. Strain through a fine sieve; discard solids. Let cool.
Whisk together flours, sugar, and 1/8 teaspoon salt. Beat whites until soft peaks form. Fold in flour mixture, browned butter, rum, and vanilla.
Coat twelve 2 3/8-inch round tart pans with cooking spray; transfer to a baking sheet. Divide batter evenly among tart shells, filling each to the top. Sprinkle each with almond slices, and bake until golden brown, 12 to 13 minutes. Brush each with jam, and let cool.