Heat oven to 350 degrees with the rack positioned near the top. Butter a deep 8-inch round, square or oval casserole generously and sprinkle all over with bread crumbs. Shake them around to coat all sides.
Place grated gruyere cheese over the bread crumbs. Add crabmeat and roasted red peppers to the top of the cheese.
Whisk together the half-and-half, whole milk, eggs, salt, pepper, tarragon, nutmeg, and chives. Pour the mixture over the cheese. Sprinkle the top with Parmesan, and bake until the top is golden and the custard is just set in the center, about 45 minutes to 1 hour. Ovens vary, you will see when the quiche has risen in the center. You can feel it with your finger, kind of like a cake. Set aside 5 to 10 minutes to cool before serving. Sprinkle with chives, cut into wedges or scoop out, and serve.