Preheat the oven to 375 degrees F. Whisk the eggs, heavy cream, 3/4 teaspoon salt and a few grinds of pepper in a large bowl until combined; set aside.
Heat 1 tablespoon olive oil in a 10-inch ovenproof nonstick skillet over medium-high heat. Add the mushrooms and cook, without stirring, until browned on the bottom, about 3 minutes. Stir, then continue cooking until the liquid evaporates, about 4 minutes. Add the remaining 1 tablespoon olive oil, the bell peppers and a pinch each of salt and pepper; cook, stirring, until the peppers are softened and lightly browned, 6 to 8 minutes.
Reduce the heat to medium. Pour the egg mixture into the skillet and stir once or twice to combine; cook, without stirring, until the edges start setting, about 1 minute. Scatter the cheese curds and scallions on top, then transfer the skillet to the oven. Bake until the frittata is set and lightly browned, 25 to 30 minutes. Let cool 5 minutes in the skillet, then invert or slide onto a cutting board. Serve warm or at room temperature.