Cook the pasta until barely al dente. Toss with olive oil and set aside. This could be made one day ahead and refrigerate until needed.
Clean the onions and separate them into green tops and white bottoms. Finely slice the green tops and set them aside. Cut the white parts into thin round slices. slice the mint basil as well, discarding the stems.
Heat a large (10-inch or larger across) sauté pan over high heat. Add a drizzle of olive oil and just as it begins to smoke add the cooked pasta. Cook over high heat for about 2 minutes, stirring frequently, and watch for some browning of the pasta. After about 2 minutes, throw in the white parts of the ramps and cook, stirring frequently, for another 2 minutes or until they begin to soften.
Add the white wine; it will immediately bubble up and nearly evaporate. Stir in the Parmesan until completely incorporated, then add the green parts of the onions. Cook for 1 more minute, or until the onions have wilted. Add the basil and immediately turn off the heat. Stir just until the basil has begun to wilt. Season to taste with salt and pepper. Add the parmesan and sir
Serve immediately with extra Parmesan, if desired.