Finely grate enough lemon peel to yield 1 tablespoon. Halve the lemons. Using an electric citrus juicer, ream the lemons to yield 1/2 cup juice.
Grease the removable bottom of a 9-inch tart pan; place the pan in the freezer. Using a food processor, coarsely chop the almonds. Add the flour, 3 tablespoons granulated sugar and 1 pinch salt and process until the nuts are finely ground. Add 4 tablespoons butter, 1 whole egg and the almond extract and pulse until a soft dough forms.
Preheat the oven to 350 degrees . Transfer the dough to the chilled tart pan and press into the bottom and up the sides. Freeze for 20 minutes.
Meanwhile, in a medium saucepan, whisk together the remaining 2/3 cup granulated sugar, 3 whole eggs and the egg yolks. Whisk in the lemon juice, lemon peel and remaining 1 pinch salt and cook over medium-low heat, stirring constantly with a wooden spoon, until the mixture thickens slightly, about 5 minutes. Remove from the heat and stir in the remaining 6 tablespoons butter until melted.
Transfer the tart shell to a baking sheet and bake until the edges are golden, about 25 minutes. Pour in the lemon filling and bake for 10 minutes. Let cool, then dust with confectioners' sugar just before serving.