Fill a pot for the pasta with about 6 quarts of water, place over high heat and bring to a boil.2.
Cut away the rind of the melon down to the orange flesh.
Cut the melon in half, discard the seeds and cut the melon into ½-inch dice.
Put the butter in a 12-inch skillet and place over medium-high heat.
Once the butter has melted completely, add the melon and season generously with salt and pepper.
Cook, stirring often, until the melon begins to break down andmost of the liquid it releases has evaporated, about 10 minutes.3.
Add about 2 tablespoons salt to the boiling pasta water, add the spaghetti and stir until all the strands are submerged.
Cook until al dente.4.
Add the tomato paste and lemon juice to the melon and stir well.
Add the cream and cook until the sauce thickens and reduces by about a third, 2 to 3 minutes.
Remove from the heat.5.
When the pasta is done, drain well, toss with the sauce and the Parmigiano-Reggiano and serve at once.