Thinly slice all shallots. Mince the garlic. Grate the Parmesan cheese.

Heat 3 tbsp olive oil and 1 tbsp butter in a large skillet or Dutch oven over medium-low heat. Add the thinly sliced shallots, 1/2 tsp salt, and 1/4 tsp black pepper. Cook slowly, stirring occasionally, for 25-30 minutes until the shallots are deeply golden brown, very soft, and sweet. Adjust the heat as needed to prevent burning.

While the shallots are caramelizing, bring a large pot of heavily salted water to a boil. Add the pasta and cook according to package directions until al dente. Before draining, reserve 1 to 1.5 cups of the pasta cooking water. Drain the pasta and set aside.

Once the shallots are beautifully caramelized, add the minced garlic and red pepper flakes (if using) to the skillet. Sauté for 1 minute until fragrant.

Pour in the white wine (or vegetable broth) and scrape up any browned bits from the bottom of the pan with a wooden spoon. Let it simmer for 1-2 minutes until slightly reduced.

Add the drained pasta, the remaining 2 tbsp unsalted butter, and 1/2 cup of the reserved pasta water to the skillet with the shallots. Toss well to combine.

Gradually add the grated Parmesan cheese, tossing constantly. Add more pasta water a splash at a time (up to 1 cup total) until a creamy sauce forms and beautifully coats the pasta. The sauce should be glossy and emulsified.

Taste and adjust seasoning with salt and pepper if needed. Serve immediately, garnished with fresh chopped parsley and extra grated Parmesan cheese if desired.