Preheat the oven to 200°C. Place the beets in a glass or ceramic baking dish. Cover with the olive oil and water. Bake until a tester easily passes through thebeetroot, about 1 1/4 hours. Let cool.
Bring a large pot of salted water to a boil.Add the spaghetti to the boiling water and cook for 8 to 12 minutes or until Al dente.
Peel the beets and cut into chunks. Add to the bowl of a food processor fitted with a metal blade and process to a rough puree.
Add the butter to a 10-inch skillet. Turn on the heat to high. Brown the butter, about 2 minutes. Add the pureed beets, salt, and the 1/4 cup pasta water to the skillet. Stir to fully incorporate.
Use a wire-mesh skimmer or tongs to remove the spaghetti from the pot and place them directly into the skillet with the sauce. Stir to combine.
Divide the spaghetti into equal portions and place on warm plates. Use two round or oval soup spoons to form little balls of the cream cheese. Place a ball on top of each serving.