Cook the pasta: If you’ve got an oven-save 3-quart deep skillet or braising pan, use it here and you’ll only need one pot for the whole recipe. Otherwise, bring an medium/large pot of well-salted water to a boil. Add pasta and cook until al dente, about 1 to 2 minutes before perfect doneness. Drain and set aside.

Heat oven to 400 degrees

Prepare the squash: Heat a large skillet or the pot you just used to cook your pasta to high heat. Once hot, add olive oil, and let it heat until almost smoking. Add sliced squash, season it with salt and pepper flakes and let it sear underneath, unmoved, until golden brown. Continue to saute until browned and somewhat wilted, about 10 minutes, trying to get some color on each layer before moving squash around. Transfer to a bowl and squeeze lemon juice over bowl. Add more salt or pepper if n...

Make the sauce: Reheat your the same pot over medium heat. Melt butter in bottom of pan. Add scallion white and pale green parts and garlic and let sizzle for 1 to 2 minutes. Add flour and stir until all has been dampened and absorbed. Add milk, a small splash at a time, stirring the whole time with a spoon. Make sure each splash has been fully mixed into the butter/flour/onion/garlic mixture, scraping from the bottom of the pan and all around, before adding the next splash. Repeat until all...

Assemble dish: Off the heat, add drained pasta, summer squash, 1/2 cup grated parmesan and all of the mozzarella to the pot, stirring to combine. If pan is ovenproof, you can bake your final dish in it. If not, transfer mixture to a 2 to 3 quart ovenproof casserole or baking dish. Sprinkle with remaining 1/4 cup parmesan.