Remove and discard the stems from the arugula leaves to be used in the pesto and the risotto. Rinse well. In a medium saucepan, bring 2 quarts of water to a boil and blanch arugula for 5 seconds. Drain and transfer to a bowl filled with ice water. After 1 minute, remove the leaves and squeeze dry with paper towel. Reserve 10 arugula leaves for the risotto. Set aside. Roughly chop the remaining leaves. Transfer to the bowl of a food processor.
Preheat the oven to 350F. Spread the walnuts to be used in both the pesto and the risotto in one layer on a baking pan. Place the pan in the oven and bake until lightly browned, about 8 minutes. Remove from the oven and place 3/4 cup of in the food processor bowl with the arugula. Transfer the remaining walnuts to a bowl and set aside.
Add the garlic, Parmigiano Reggiano, and ricotta to the food processor bowl and turn the machine on. When the mixture is blended, with the motor still running, slowly pour the oil into the feed tube. Process until smooth and emulsified, about 1 minute. Season with salt and pepper to taste. Reserve in a small squirt bottle at room temperature.
Prepare the risotto: In a medium skillet, heat 2 tablespoons of the olive oil over medium-high heat. When hot, add the mushrooms and cook, stirring occasionally, until tender, 8 to 10 minutes. Remove from the heat, transfer to a bowl and set aside. In a large saucepan, combine the onion, garlic, and remaining olive oil and cook over medium heat, stirring often, until the onion is soft, about 10 minutes. Add the rice and “toast” it, stirring constantly for 1 minute. Add the white wine and cook, evaporating the liquid by half. Pour in 2 cups of the stock and cook at a low boil, stirring constantly, until the liquid is absorbed. Continue to add the stock to the rice, 2 cups at a time, until all of the stock has been added. After a total cooking time of about 15 minutes the rice should be moist and creamy. Remove from the heat and whip in the Parmigiano Reggiano and the butter. Season with salt and pepper to taste. Fold in the reserved portobello mushrooms and walnuts.
To serve, mound a portion of risotto in the center of each plate. Decoratively squeeze the Arugula Pesto around the base of the rice. Garnish with the diced tomatoes and a blanched arugula leave.