For the carrot purée:

2 1/2 quarts water
1 tablespoon kosher salt
12 ounces carrots (about 4 to 5 medium), peeled and cut into 1/2-inch dice

For the broth:

1 1/2 pounds carrots, cut into large chunks
1 medium celery stalk, coarsely chopped
1 medium yellow onion, coarsely chopped
3 medium garlic cloves, smashed
1 fresh thyme sprig
1 bay leaf

For the risotto:

1/4 cup olive oil
1 medium yellow onion, finely chopped
3 medium garlic cloves, minced
1 teaspoon finely chopped fresh thyme
Freshly ground black pepper
2 cups short-grain rice, such as Arborio or Carnaroli
1 teaspoon kosher salt, plus more for seasoning
1/2 cup dry white wine
12 ounces carrots (about 4 to 5 medium), peeled and shredded on the large holes of a box grater
1/4 cup grated Parmesan cheese (grated on the small holes of a box grater), plus more for serving
3 tablespoons unsalted butter
1 to 2 tablespoons freshly squeezed lemon juice