Place spaghetti in a large pot of salted boiling water. Stir occasionally to prevent sticking. Cook until al dente, according to package directions (usually around 8-9 minutes). *Don't drain without reading step 6.
While the pasta is boiling, heat olive oil in a large skillet over medium heat. When hot, add the garlic and crushed red pepper flakes. Sauté for 2-3 minutes until the garlic is softened, fragrant, and barely golden. You don't want to brown the garlic, so stir often and lower heat if necessary.
Add the tomatoes, salt, and fresh cracked pepper to the pan over medium heat. Cook for 5-7 minutes, until the tomatoes soften and release their liquid. The liquid should start to simmer and slightly thicken. Don't let it simmer too high or the liquid will reduce too much. If things are looking dry, you can add a few tablespoons of pasta water from the boiling pot into the tomatoes.
Pour in the white wine and simmer for 2-3 minutes to reduce slightly. If the wine smells strong in the sauce, give it another minute to simmer to meld the flavors.
Now add the feta cheese and half the basil. Stir and let it cook until the cheese melts into the sauce. Taste for seasoning and add more if needed.
Once the pasta is cooked, reserve ½ cup of pasta water and set aside. Drain the pasta and drizzle with olive oil to prevent sticking.
Now add the pasta along with only half of the pasta water into the pan. Toss to coat well. Gently simmer until sauce is slightly thickened and silky. Add the remaining pasta water if needed. The pasta should be well coated in the sauce. Top with the remaining basil and more feta if desired. Serve immediately.