Bring a pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1/2 cup of the cooking water.
While the pasta is working, in a large skillet, heat the EVOO, 3 turns of the pan, over medium heat. Add the butter to melt until foaming. Add the shallots and garlic and cook for 2 minutes; season with salt and pepper. Add the ham and cook until lightly browned, 2 to 3 minutes.
Stir the wine into the ham mixture and cook, swirling, to reduce by half. Stir in the cream and season with nutmeg. Stir in the peas and tarragon. Remove the sauce from the heat.
Add the pasta and some cheese to the sauce; toss, stirring in the reserved cooking water to thin the consistency if desired. Season with salt and pepper and top with more cheese.