Combine 1 2/3 cups all-purpose flour, 1/2 cup almond flour, 7 tablespoons white sugar, and 1/2 teaspoon salt in a bowl. Mix in 1/2 cup cold butter using your fingers until the mixture resembles coarse crumbs. Form a well; pour in beaten egg. Mix until a dough forms; knead until just combined. Wrap dough in plastic wrap; freeze for 15 to 20 minutes.
Beat 1/2 cup superfine sugar and 7 tablespoons butter together in a bowl using an electric mixer until creamy. Stir in 1 cup almond flour and 3 1/2 tablespoons all-purpose flour. Add egg yolk; mix until frangipane is well combined.
Place 3 cups strawberries and 1/3 cup white sugar in a pot over medium heat. Cook and stir until mixture starts to simmer. Reduce heat to low; mash strawberries. Cook until jam is thickened, 10 to 15 minutes more. Strain through a fine sieve; reserve pulp. Allow to cool.
Preheat oven to 400 degrees F (200 degrees C).
Flour a work surface and a rolling pin; roll dough out to a 1/8-inch thick circle and place in a tart pan. Line crust with a double layer of aluminum foil and a layer of pie weights or dried beans.
Bake in the preheated oven for 10 minutes.
Carefully remove weights and foil; add frangipane, spreading into a layer 1/3 the thickness of the crust.
Return to the oven; bake until golden brown, 15 to 20 minutes. Let tart cool for 5 minutes.
Spread reserved pulp over tart; press in strawberries to cover surface. Pour jam evenly over the tart. Cool until set, about 30 minutes.