Step 1: Cook pasta according to package directions in a large pot of salted boiling water until al dente. Before draining, reserve about 1 cup of pasta water.
Step 2: While pasta cooks, heat olive oil in a large skillet or Dutch oven over medium heat. Add chopped onion and cook until softened and translucent, about 3-5 minutes.
Step 3: Add minced garlic to the skillet and cook for another minute until fragrant, being careful not to burn.
Step 4: Stir in the gochujang paste and cook for 1-2 minutes, stirring constantly, to bloom its flavors.
Step 5: Pour in the crushed tomatoes, vegetable broth, and soy sauce. Bring the mixture to a gentle simmer, then reduce heat to low, cover, and let simmer for 10-15 minutes, allowing flavors to meld. Stir occasionally.
Step 6: Stir in the heavy cream and Parmesan cheese (if using). Continue to simmer for 2-3 minutes, or until the sauce has thickened slightly. Season with salt and black pepper to taste. If the sauce is too thick, add a splash of reserved pasta water.
Step 7: Add the drained pasta directly to the sauce in the skillet. Toss thoroughly to coat every strand. Add a little more reserved pasta water if needed to achieve desired consistency.
Step 8: Serve immediately, garnished with fresh chopped green onions and a sprinkle of sesame seeds. A drizzle of sesame oil is optional for extra aroma.