In a 4- or 5-quart Dutch oven or heavy sauce pan, combine the olive oil and butter over medium heat. Add the shallot and garlic and cook, stirring, for 1 minute, until just softened. Add 2 cups of the peas, plus the oregano. Cook, stirring to keep the peas from sticking, for 2 minutes. Pour in the broth, and raise heat to high. Bring to the boil, then reduce heat to simmer, cover, and cook for 10 minutes.
Remove the pot from the heat and, with an immersion blender, puree until smooth. (Or, if you're using a stand blender, let the soup cool for a few minutes, then puree in batches, and return to the pot.).
Stir in the remaining 1/2 cup of peas, and the pasta. Again, bring the soup to the boil over high heat, and reduce heat to simmer. Cook for 5 minutes, uncovered, stirring often to keep the pasta and whole peas from sticking. If the soup is thickening too much, add 1/2 cup of water. After 5 minutes, grate the cheese directly into the pot with a Microplane® or box grater, and season with salt and pepper to taste (this soup loves quite a bit of black pepper, so don't be timid).
Continue cooking for 5 minutes more, or until the pasta is soft. If the soup is too thick, add more water or stock to achieve the texture you like.
Ladle into individual serving bowls, and garnish with grated cheese.