In a large pot, bring 4 quarts water and 2 tablespoons salt to a boil. Peel the broccoli stems, reserving any leaves, and cut crosswise into ½-inch rounds. Add the stems and leaves to the boiling water and cook until fully tender, about 10 minutes. Stir in the spinach and cook until wilted, about 20 seconds. Using a slotted spoon, transfer the vegetables to a blender; reserve ½ cup of the cooking water. Keep the water at a boil.