Heat the oil and butter in a large skillet over medium-high heat. Once the butter has melted, add the onions and sauté until translucent, about 3 minutes. Add the garlic, oregano and crushed red pepper flakes and cook for about 1 minute more. Add the entire can of crushed tomatoes and bring the mixture to a boil over high heat, then reduce to a simmer for 20 minutes, stirring occasionally, until thickened. Season with salt and pepper.
In 1 batches, transfer the sauce to a blender and add the cream and vodka. Remove the center knob on the lid (to allow steam to escape) and place a towel over the lid to prevent splattering. Slowly (starting on the lowest setting and increasing every few seconds), blend until completely smooth, about 30 seconds. Return to the saucepan and bring just to a boil over high heat to cook off the vodka. Once boiling, reduce to a simmer.
Meanwhile, cook the pasta until al dente. Drain the pasta, reserving 1 cup of the cooking water, then add the pasta to the sauce with the shredded mozzarella. Stir to combine, and cook over medium heat, stirring frequently, adding some of the reserved pasta cooking water as needed to thin it out. (you might not need any of the reserved pasta water if you don't need to thin the sauce FYI). Taste and adjust seasoning with salt and pepper as needed.
Serve immediately, topped with Parmigiano-Reggiano (to taste).