Step 1In a medium bowl, whisk together the minced shallots, lemon juice, vinegar, salt and pepper. Slowly whisk in the olive oil, then the mustard. This makes about one-third cup dressing. Cover and refrigerate until needed, up to 5 days. Whisk again to emulsify before using.
Step 1Adjust the oven rack to the middle position and heat the oven to 400 degrees.
Step 2To cook the beets, trim and discard the tops of the beets and scrub thoroughly. Pat the beets dry with paper towels and place them in a baking dish large enough to fit them in a single layer. Drizzle the beets with the olive oil, season them with the salt and pepper to taste and toss to coat the beets with the seasonings. Cover the dish with foil and place it in the oven to cook the beets until they can be easily pierced with a knife, about 1 hour. Remove the beets from the oven, and remove the foil, being careful not to burn yourself from the steam that will arise from the baking dish, and set the beets aside until they are cool enough to the touch. Rub the beets with a clean dish towel to remove their skins and cut the beets into one-fourth-inch cubes. Toss with enough dressing to coat.
Step 1In a medium bowl, whisk together the minced shallots, lemon juice, vinegar and salt. Slowly whisk in the olive oil, then the walnut oil. This makes about three-fourths cup dressing for the salad; more than is needed for the remainder of the recipe. Cover and refrigerate until needed, up to 5 days. Whisk again to emulsify before using.
Step 2In a large bowl, toss the beet greens and walnuts with enough dressing to barely coat. Taste and adjust the seasonings if desired.
Step 3To serve, divide the salad among four plates. Place 2 ounces of burrata (use either one 2-ounce ball with the top of the skin removed or half of a 4-ounce ball) in the center of each plate. Divide the beets, piling them evenly over the cheese (use a large soup spoon to scoop up the beets and press them tightly into the spoon, then invert the spoon carefully over the cheese to mound the beets on top.) Grate fresh horseradish over the top of each and serve immediately.