Topping: process the bread and butter in a food processor with steel blade until coarsely ground, about six 1-second pulses.
Filling: adjust an oven rack to the middle position and heat oven to 400 degrees. Toss the zucchini and summer squash with 2 T kosher salt and place in a large colander set inside a large bowl to drain, about 30 minutes.
Bring 4 quarts of water to boil in a dutch oven over high heat. Stir in 2 T kosher salt and the pasta. Cook, stirring occasionally until al dente. Drain, return to the pot and toss with
1 T oil. Set aside.
Spread the salted squash evenly over a double layer of paper towels and pat dry with additional paper towel, wiping off any residual salt. Heat 1 more tablespoon oil in a 12” nonstick skillet over high heat until smoking. Add have the squash and cook, stirring occasionally until golden brown and slightly charred, 5-7 minutes. Transfer the squash to a baking sheet. Add 1 more T oil to the pan, return to high heat until smoking and brown the remaining squash. Transfer to baking sheet when finished.
Wipe the skillet clean with a wad of paper towels. Add the remaining T oil and return to medium-high heat until shimmering. Add the shallots and cook until softened, about 3 minutes. Add the garlic and cook until fragrant, about 30 seconds. Add the flour and cook, stirring constantly, until golden, about 1 minute. Slowly whisk in the broth and cream; bring to a simmer and cook, whisking often, until lightly thickened – about 1 minute. Off the heat, stir in parmesan, basil and parsley. Season with salt and pepper to taste.
Add the sauce, tomatoes and sautéed squash to the pasta; stir gently to combine. Pour the pasta into a 9x13” baking dish (or a shallow casserole dish of similar size) and sprinkle with breadcrumb topping. Bake until the casserole is bubbling and the crumbs are lightly browned, about 15 minutes. Serve immediately.
