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.
You can use milk or even light milk for those who want a lighter version. Tapioca flour can be found in specialty gluten-free shops.
You can substitute 2 cups Parmesan cheese and 1 pinch sea salt for the Pecorino-Romano cheese.
If this recipe is too challenging there is a wonderful company called Yoki(R) that make a pre-packaged version that is fantastic.