Preheat the oven to 300°. Line a 12-by-17-inch rimmed baking sheet with parchment paper and spray with vegetable oil cooking spray.
In a saucepan, melt 7 tablespoons of the butter. Add the all-purpose flour and cook over moderately high heat, whisking, until lightly browned, 2 minutes. Whisking constantly, add the semolina and cook for 1 minute. Off the heat, gradually whisk in the milk and cream. Cook over moderately high heat, stirring constantly, until thickened, 5 minutes.
Transfer 1 cup of the hot mixture to a large bowl and whisk in the egg yolks. Whisk in the remaining hot mixture, then whisk in the Parmesan and cayenne and season with salt and pepper.
In another large bowl, using an electric mixer, beat the egg whites with the cream of tartar at medium speed until frothy. Increase the speed to high and beat until soft peaks form. Beat one-fourth of the whites into the yolk mixture, then fold in the remaining whites until no streaks remain.
Spread the batter in the baking sheet and smooth the surface. Bake for 30 minutes, or until the omelet is risen and puffed and small cracks appear on the surface. Let the omelet cool in the pan.
Meanwhile, heat a large skillet. Add the spinach in large handfuls and cook over high heat until wilted, allowing each batch to wilt slightly before adding the next. Transfer to a strainer and press out as much liquid as possible. Coarsely chop the spinach. Wipe out the skillet and melt the remaining 1 tablespoon of butter. Add the garlic and cook over moderate heat, stirring, until softened. Add the spinach, season with salt and pepper and cook, stirring, for 1 minute.
Cover the omelet with a sheet of wax paper and a clean kitchen towel. Place a cookie sheet over the omelet and invert it onto a work surface with the long side facing you. Remove the rimmed baking sheet and carefully peel off the parchment paper.
Arrange the spinach along the bottom edge of the omelet in a 3-inch strip. Dollop the goat cheese over the spinach. Using the kitchen towel as a guide, roll the omelet up like a jelly roll, peeling back the wax paper as you go. Carefully roll the omelet onto a long platter. Using a large spatula, tuck any omelet under that may have unrolled. Cut into slices and serve.
The omelet can be made up to 3 hours ahead and served at room temperature or rewarmed for 10 minutes on an ovenproof platter in a 300° oven.