Add the oil and shallots to a large, high-sided saute pan over medium heat. Sprinkle with a pinch of salt, then cover and sweat (do not caramelize) for 2 to 3 minutes. Add the rice and toast for about 5 minutes, stirring to coat the grains with oil. Add the garlic and cook, stirring, until aromatic. Deglaze the pan with the red wine.
Meanwhile, in a medium saucepan, warm the beet juice and vegetable stock. Slowly add the beet juice mixture to the risotto pan, one ladle at a time, stirring and adding ladlefuls only once the previous has been absorbed. Cook in this manner until the rice is tender and all the liquid has been added, 30 to 40 minutes.
Stir in the butter and then the pecorino. Taste for seasoning and adjust as needed. Serve garnished with Roasted Red Beets, more pecorino, and chives.
Preheat the oven to 350 degrees F. Place the beets in the center of a large piece of foil and drizzle with the olive oil. Add the garlic, rosemary and some salt and pepper. Crimp the edges of the foil together to seal. Roast until tender, 40 minutes. When cool enough to handle, remove the skins and cut the beets into dice.