Preheat oven to 450°F. Fit the refrigerated pie crust into a 9-inch pie plate and crimp or flute the edges.
Line the crust with aluminum foil, pressing the foil against the bottom and sides to hold the crust shape. Bake the lined crust for 5 minutes.
Remove the foil and bake the crust for an additional 5 minutes. Immediately sprinkle 1/2 cup of the shredded Swiss cheese evenly over the warm crust. Reduce oven temperature to 375°F.
While the crust is baking (or after, if you prefer), melt the 1 tablespoon unsalted butter in a skillet over medium heat. Add the 1/2 cup chopped sweet red pepper and 1/4 cup chopped green onions and sauté until softened, about 3–4 minutes. Remove from heat.
In a mixing bowl, whisk together the 3 large eggs, 1 1/2 cups half-and-half, 1/2 teaspoon salt, and 1/4 teaspoon black pepper until combined.
Fold the sautéed red pepper and green onions, the 3/4 cup chopped flaked imitation crabmeat, and the remaining 1/2 cup shredded Swiss cheese into the egg mixture.
Pour the filling into the prepared pie crust, spreading gently to level.
Bake the quiche at 375°F for 30–35 minutes, or until the center is set and a knife inserted in the center comes out clean.
Remove the quiche from the oven and let it rest for 15 minutes before slicing and serving.