Slice the ramps in half crosswise, separating the whites and greens into separate parts. Very roughly chop the bulbs, leaving some large pieces. Very roughly chop the leaves, leaving most of the greens in large pieces.
Heat the olive oil in a large skillet over medium heat. Add the white ramp bulbs, season with salt and pepper, and sauté for about 8 minutes, then add the leaves and sauté everything for another 5 or 6 minutes until the ramps are quite tender.
Meanwhile, bring a large pot of water to a boil. When it comes to a boil, add a generous amount of salt. Add the pasta and cook according to package directions, just until al dente. Just before draining, remove 1 cup of the cooking water. After draining, return the pasta to the pot.
When the ramps are tender, turn the heat to high, add the white wine, stir to reduce the wine by half, and deglaze the pan. Scrape the ramps and remaining wine into the pot with the drained pasta, and place the pot over high heat. Add the chicken broth, red pepper flakes, and about 1/2 cup of the cooking water. Stir and toss until the liquid reduces a bit into a sauce and absorbs into the pasta, and the pasta becomes tender; add more of the cooking water as needed/desired. Add the heavy cream, toss for another minute, then add the cheese. Stir until it melts into the sauce and everything is hot and well combined.
Serve hot, with extra grated Parm, if desired.
Notes
Before cooking ramps, you need to remove all the dirt. Rinse thoroughly in cold water and use your hands to get any clumps out of the ramp's roots. Alternatively, submerge the ramps in a large bowl of cold water (or in the sink) and swish them around until the dirt is gone. Rinse one more time before trimming the roots and cutting the ramps for the recipe.