Arrange two racks in the oven, a lower rack for a braiser pan and an upper rack for a backing dish. Preheat oven to 375 degrees Fahrenheit.
Separate the beet roots, stems and greens. Rince, peel and chop the roots into 1/2" dice. Rince the stems, dice, and hold the stems with the diced onions and green garlic. Roughly chop the leaves, wash them and dry with a salad spinner.
Place an enameled cast iron braiser on the stovetop at medium-high heat. Sauté chorizo with about 1 tablespoon of olive oil, rendering the fat from the sausage.
Add the diced onion, beet stems and green garlic with ½ teaspoon of salt and stir. If there isn’t enough oil to make everything glisten, add another splash. Sauté until the onions are softened and translucent.
While things are sautéing, toss the chopped beet roots with 1/2 teaspoon of salt and 1 tablespoon of olive oil. Then spread them out evenly on a rimmed baking sheet.
Make a well and add tomato paste to the center of the well. After a minute or two, stir together the aromatic mixture.
Add the rice and coat it well with the aromatic mixture. Stir in the saffron, paprika and 1/2 teaspoon of salt.
Add the dry white wine and use a wooden spatula to deglaze any fond that developed during the previous steps.
Add the broth and stir. Turn the heat up to high, and bring to a boil. Once at a boil, stir in the chopped beet leaves.
Cover the pot and place on the lower rack in the oven. Also place the baking pan on the upper rack in the oven. The pot will cook for 50 minutes. The beets will likely be done in 40 minutes. Remove the beets when they are fully roasted and tender.
Remove the pot from the oven. Stir in the roasted beet roots. Serve hot. Optionally garnish with parsley or chives.