In a large pot, cook fettuccine as directed. Towards the end of the pasta cooking, add the broccoli into the pot to cook for approximately 3–4 minutes.
In a greased large saucepan, heat garlic on medium-high heat for 2 minutes.
Add red pepper flakes, ginger, and brown sugar into the saucepan. Allow to cook another 2 minutes.
Add soy sauce, rice wine vinegar, and peanut butter to the saucepan. Use a spaghetti spoon or whisk to mix in the peanut butter to the liquid to form a sauce.
When the sauce begins to bubble, add the cooked pasta/broccoli to the saucepan. Mix well. Add the carrot. Mix well to prevent clumps.