Pistachio Brown Butter Cake with Concord Grapes

Martha Stewart's pistachio brown butter cake recipe with Concord grapes appears in the "Fruit Desserts" episode of Martha Bakes.

1 cup (2 sticks) unsalted butter, cut into small pieces, plus more for pan
2 ¾ cups confectioners’ sugar
1 cup pistachio flour or 1 cup unsalted pistachios and 1 tablespoon unbleached all-purpose flour
¾ cup cake flour
1 teaspoon coarse salt
7 large egg whites (3/4 cup plus 2 tablespoons)
1 heaping cup halved, seeded Concord grapes
2 tablespoons Demerara sugar

Melt butter in a small heavy-bottomed saucepan over medium heat. Continue cooking until light brown and smells nutty, about 6 minutes. Remove from heat and strain through a fine mesh sieve into a bowl.
In a large bowl, sift together confectioners’ sugar, pistachio flour (or pistachios and flour processed in a food processor until fine), cake flour, and salt. Whisk in egg whites to combine. Whisk in strained butter in a slow, steady stream. Cover bowl with plastic wrap and refrigerate until thickened, about 1 hour and up to 1 week.
Preheat oven to 350 degrees. Generously butter a 9-inch fluted tart pan with a removable bottom.
Pour chilled batter into prepared tart pan. Sprinkle grapes over the top, keeping fruit ½ inch in from the edge of the pan. Sprinkle grapes and batter with Demerara sugar.
Place tart pan on a baking sheet and bake until edges of the cake are dark golden brown and top is slightly springy to the touch, 1 hour and 15 minutes to 1 hour and 30 minutes. Transfer cake to a wire rack, remove the outer ring of the pan, and let cool; serve warm or at room temperature. This cake is best eaten the day it is made, but can be kept at room temperature, loosely covered with plastic wrap, for up to 2 days.