Heat half-and-half, vegetable, and salt together in a saucepan over medium heat; constantly whisk until mixture just starts to boil, about 5 minutes. Remove from heat and pour mixture into a large deep bowl.
Stir tapioca flour into half-and-half mixture using a wooden spoon. Mixture will thicken quickly. Cool to room temperature, about 20 minutes.
Preheat oven to 350 degrees F (175 degrees C).
Mix Pecorino Romano cheese and eggs into tapioca mixture using an electric mixer or by hand until dough has a paste-like texture. Continue mixing until dough is soft and stretchy. Roll dough into 2- or 3-inch balls and arrange on a baking sheet.
Bake in the preheated oven until cheese balls are puffed and hardened on the outside, 20 to 25 minutes. Serve warm.