Make the pesto: In a food processor or with a large mortar and pestle, combine all of the pesto ingredients. Process into a rustic pesto. Set aside.
Prepare the polenta: Bring the water to a boil in a heavy-bottomed pot over medium heat. Whisk in the polenta and salt. Bring it up to a boil, then turn the heat down to low.
Simmer the polenta for 30–40 minutes, stirring often, until it is thickened and fully cooked.
Remove the pot from the heat. Stir in the mascarpone and Parmesan cheese.
To serve: Pour the polenta out into a large, shallow serving bowl. Dollop the pesto onto the polenta and swirl it in with a spoon. Toss the arugula with the oil, vinegar, salt and pepper. At the last minute, arrange it on top of the polenta in a big pile and serve family style.