1. Preheat oven to 400 degrees F. Line 2 large baking sheets with parchment paper. Bring butter and 1 cup water to a boil in a large heavy saucepan. Remove from heat. Add flour, cayenne, and salt; stir vigorously to blend. Return to heat; stir vigorously over medium heat until mixture forms a ball and a thin, dry film forms on the bottom and sides of pan about 1 minute. Transfer mixture to a stand mixer fitted with a paddle attachment. Add 1 cup Gruyere, Asiago and 2 teaspoons thyme; beat on low speed to blend. Add 4 eggs, one at a time, fully incorporating each egg between additions, and scraping down sides of bowl as needed. 2. Spoon dough into a pastry bag fitted with a 1/2 inch tip or a plastic bag with a 1/2 inch cut diagonally from 1 corner. Pipe dough onto prepared baking sheets in 1 - 1 1/4 inch rounds, spacing 1 inch apart. Whisk remaining egg with 1 tablespoons water in a small bowl. Brush egg wash lightly over rounds, patting down to form rounded tops. Sprinkle with remaining 3 tablespoons Gruyere. Garnish each with a few thyme leaves. 3. Bake gougeres until puffed and golden brown and centers are cooked through but still moist, 20 - 25 minutes. Let cool slightly and serve. ---------------------------------------------------------------------------
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