Bring a large pot of generously salted water to a rolling boil. Cook spaghetti until al dente according to package directions. Reserve 1 cup of pasta water, then drain.
While pasta cooks, warm olive oil in a large skillet over medium-low heat. Add minced garlic and cook until fragrant but not browned, about 1 minute. Remove from heat.
In a medium bowl, combine the ricotta, lemon zest, lemon juice, Parmesan, salt, and pepper. Whisk until smooth and creamy.
Return the skillet with garlic oil to low heat. Add the drained spaghetti and toss to coat in the oil. Pour the ricotta mixture over the pasta and toss quickly, adding pasta water a few tablespoons at a time, until a silky, thin sauce clings to each strand.
Remove from heat. Fold in torn basil leaves, then divide among bowls. Top with extra Parmesan, lemon zest, black pepper, and a drizzle of olive oil. Serve immediately.