If using baby spinach and arugula, rinse in colander. If using bunched spinach and arugula, soak the spinach and arugula leaves separately in a bowl of cold water for 30 minutes to let the grit and sand settle.
Heat a 10- to 12-inch skillet over medium heat. Toss in the spinach, with water from rinsing still on the leaves. Cook, stirring, until wilted, several minutes. Place the spinach in a colander and drain well. Then finely chop it.
Drain the arugula leaves and roughly chop it.
Place the stock in a saucepan and bring to a boil. Reduce the heat to a simmer. Skim off any scum that rises to the surface.
In a 6-quart non-reactive saucepan, heat the olive oil and butter until the butter melts. Add the shallots and garlic and stir over low heat for 2 minutes. Add the rice and continue to stir until the rice is translucent, about 1 minute.
Add the wine and cook over medium heat until all the liquid has been absorbed. Then stir in 1 teaspoon salt.
Using a ladle, add 1/2 to 1 cup warm stock and stir frequently after each addition until the stock has been almost completely absorbed. Repeat until almost all the stock has been absorbed and the rice is al dente, 27 to 32 minutes. You may only need 4 1/2 cups stock.
Stir in the chopped spinach, chopped arugula, chopped parsley, and peas. Cook for 4 minutes, stirring occasionally.
Remove from the heat and stir in the heavy cream and 1/2 cup of the Parmigiano. Taste and season with the red pepper and add salt and black pepper..
Serve immediately, passing the remaining Parmigiano separately.