In a deep skillet, cook the peas with ½ cup of water, the garlic and 3 tablespoons of olive oil. Season with salt and the sugar.
In a separate skillet, melt the butter. Add the ham and cook for a couple of minutes. Add the pea mixture and stir.
Add the heavy cream, season with salt and pepper and cook over high heat.
Cook the pasta in salted boiling water until al dente. Drain and add to the sauce, toss and serve with the Parmesan on the side. As an alternative, add 100gr. Of diced chicken breast to the ham.