Combine the olive oil and 1 1/2 tablespoons pepper in a small saucepan and cook over medium heat until just starting to bubble, 3 to 5 minutes. Put the spaghetti in a medium bowl and pour the olive oil mixture over the top. Mix to combine and set aside.
Combine the flour, 1 1/2 tablespoons salt, the baking powder and baking soda in a large bowl. In a separate bowl, whisk the buttermilk and egg yolks. Form a well in the center of the dry ingredients and add the buttermilk mixture. Whisk until the batter is well combined (there will still be some small lumps).
Add the spaghetti, pecorino and mozzarella to the batter. Mix well with a rubber spatula.
Preheat the oven to 250 degrees F. Fill a large skillet with about 1/2 inch olive oil and heat until a deep-fry thermometer registers 325 degrees F. Working in batches, scoop the spaghetti mixture into the skillet (about 2 tablespoons per fritter); flatten slightly with a metal spatula. Fry the fritters, flipping once, until golden brown and warmed through, about 4 minutes. Remove to a paper towel-lined plate to drain, then transfer to a baking sheet and keep warm in the oven while you fry the remaining fritters. Top with more pecorino before serving.