Buttermilk blueberry puff

12 tablespoons unsalted butter, at room temperature, plus 1 tablespoon for the baking dish
12 cups cubed croissants (6 to 8 large)
3 cups blueberries or blackberries
1 cup granulated sugar
6 large eggs, at room temperature
2 cups heavy cream
1 cup buttermilk
2 tablespoons pure vanilla extract
1 teaspoon kosher salt
1 tablespoon coarse raw (turbinado) sugar

Preheat the oven to 375 degrees. Grease a 9-by-13-by-3 baking dish with the 1 tablespoon butter. Spread the croissant cubes evenly in the dish. Top with berries. In a stand mixer fitted with the paddle attachment, beat the 12 tablespoons butter with the granulated sugar on medium speed until creamy. Beat in the eggs, one at a time, beating well after each addition. Beat in the cream, buttermilk, vanilla and salt. The mixture may appear curdled. Pour over the croissants and berries in the baking dish. Sprinkle with the coarse sugar. Bake until a knife inserted near the center comes out clean, about 35 minutes. Serve warm. The puff is best eaten warm, soon after baking, but leftovers can be covered and stored in the refrigerator for up to two days.