Combine 6 cups cherries, 6 tablespoons sugar, and lemon zest in a bowl. Allow cherries to rest for 2 to 3 hours.
Preheat oven to 425 degrees F (220 degrees C). Line a baking sheet with parchment paper.
Mix flour, 1/4 cup sugar, cream of tartar, baking soda, cinnamon, cardamom, and salt in a large bowl. Cut in butter with a knife or pastry blender until the mixture resembles coarse crumbs. Whisk egg and half-and-half in a small bowl; stir into the flour mixture with a fork until dough is moistened with large clumps. Add a teaspoon more half-and-half to the bowl if dough won't come together.
Roll tennis ball size scoops of dough and place on prepared baking sheet. Press each ball down lightly to form 1/2-inch discs. Brush dough with egg white and sprinkle with 1 teaspoon sugar.
Bake in preheated oven until golden brown, 12 to 14 minutes. Cool in the pan for 10 minutes before removing to cool completely on a wire rack.
Slice each cake in half horizontally. Layer a generous portion of halved cherries, almonds, and whipped cream between cake halves. Top with another dollop of whipped cream, almonds, and a whole cherry.