Step 1

Preheat the oven to 350 degrees F.

Step 2

Grease a 2-quart baking dish with 1 tablespoon butter. Set a colander over the sink or a large bowl.

Step 3

Melt 2 tablespoons butter in a large heavy-bottomed skillet over medium-high heat. Add half of the squash and onion; do not salt yet, as you want the vegetables to brown a little. Cook, stirring often, until the center of the squash is just tender, 8 to 10 minutes. Set aside on a sheet tray or large bowl and repeat with 2 more tablespoons of butter and the remaining squash and onions.

Step 4

Combine the squash and onions and season with 1 teaspoon of salt and a bit of pepper, taking care not to break up the squash too much.

Step 5

(Alternatively, you can toss the vegetables with 4 tablespoons melted butter and distribute them between two sheet pans and roast at 400 degrees F for 25 to 30 minutes.)

Step 6

Transfer the squash and onions to the colander and drain for 5 minutes; discard any liquid.

Step 7

Stir together the eggs, crème fraîche, Gruyère, Cheddar, mayonnaise, thyme, mustard, cracked pepper and remaining teaspoon salt in a large bowl.

Step 8

Gently fold in the squash mixture until evenly combined. Spoon the casserole filling into the prepared baking dish.

Step 9

Microwave the remaining 3 tablespoons butter in a medium microwavable bowl until melted, about 25 seconds.

Step 10

Toss the breadcrumbs, Parmesan, melted butter and 1/4 cup parsley in a small bowl until combined. Taste and season with salt and pepper.

Step 11

Distribute the breadcrumb topping evenly over the casserole. Bake until golden brown, 20 to 25 minutes.

Step 12

Garnish with the remaining 2 tablespoons parsley.