Place ½ tablespoon of the unsalted butter in an 8x11-inch or other 2-quart baking dish and set aside to let the butter come to room temperature. Using a mandoline or chef's knife, trim and very thinly slice 1 ½ pounds zucchini and 1 ½ pounds yellow summer squash crosswise. Place in a colander, sprinkle with 1 ½ teaspoons of the kosher salt, and toss to combine. Place the colander in the sink or over a large bowl and let the squash drain for 20 minutes. Meanwhile, heat the oven and make the béchamel sauce.

Arrange a rack in the middle of the oven and heat the oven to 350ºF. Finely chop 4 garlic cloves. Melt the remaining 4 tablespoons unsalted butter in a medium saucepan over medium heat. Add the garlic and cook, stirring occasionally, until fragrant, about 1 minute. Add ¼ cup all-purpose flour and cook, whisking, until the garlic and flour are lightly toasted, about 2 minutes.

While whisking constantly, slowly pour in the 3 cups milk. Increase the heat to medium-high and bring to a boil, stirring constantly. Reduce the heat to maintain a simmer and cook, whisking often, until the sauce thickens significantly, 5 to 10 minutes. Remove from the heat. Add ½ teaspoon paprika, ¼ teaspoon dry mustard, the remaining ¼ teaspoon kosher salt, and ¼ teaspoon black pepper, and whisk to combine.

When the squash is ready, working with a heaping handful at a time, place in a clean kitchen towel or paper towels and squeeze as much water as possible from the squash, then place in a bowl. Shred 8 ounces fontina cheese on the large holes of a box grater.

Coat the baking dish with the softened butter. Spread ½ cup of the béchamel sauce in the bottom of the baking dish. Spread half of the squash over the cream sauce in an even layer. Drizzle with half of the remaining béchamel sauce (about 1 cup), then sprinkle with half of the fontina. Layer on the remaining squash, béchamel sauce, and fontina.

Place ½ cup panko breadcrumbs, ¼ cup grated Parmesan cheese, and 2 teaspoons olive oil in a small bowl, season with a pinch of kosher salt and black pepper, and stir to combine. Sprinkle evenly over the casserole.

Bake until the sides of the casserole are bubbling, about 40 minutes. Check after 30 minutes and tent the casserole loosely with aluminum foil it the top is already browned before continuing baking. Let rest for 15 minutes before serving.