In a large (at least 12-inch) cast iron skillet over medium-high heat, melt the butter and oil. When it’s foaming, add the zucchini, garlic, the basil stems and half the basil leaves. Season with 1 1/4 teaspoons salt and a few grinds of pepper. Cover and cook until pooling with liquid, 5 to 7 minutes. Uncover and cook until the liquid evaporates and the zucchini starts to sizzle, 7 to 10 minutes.
Continue to cook until the zucchini is very soft, dark green, and reduced to about 1 cup, another 20 to 25 minutes. When you see a build up of browned bits on the skillet, add a couple tablespoons of water and stir, scraping up the browned bits. Repeat anytime more browning occurs. If you see burning, deglaze with water and lower the heat. (Caramelized zucchini can be made ahead and refrigerated for up to a week; it also freezes well.)
Meanwhile, bring a large pot of salted water to a boil. When the zucchini is about done, add the pasta to the boiling water and cook until al dente. Reserve 2 cups of pasta water, then drain the pasta. If the zucchini is ready before the pasta, keep cooking it; the zucchini will only get better the longer it cooks.
When the pasta’s drained, remove the herb stems from the zucchini. Reduce the heat on the zucchini to medium, then add the pasta, 1 cup pasta water, and the Parmesan. Stir until the pasta is glossed with sauce. Add more pasta water as needed to thin the sauce. Stir in the lemon juice and remaining basil, then season to taste with salt and pepper. Serve with more basil, Parmesan and black pepper.