Brush asparagus with 2 tablespoons of the oil and season with salt and pepper to taste. Grill for 4 to 5 minutes, until just cooked through. Cut on the bias into 1/2-inch pieces. Set aside.
Use side burner or preheat grill. (Have stock simmering on grill or burner) Heat the oil in a medium saucepan, add the onions and shallots and cook until soft. Add the rice and stir to coat with the oil. Add the wine and completely reduce. Begin adding the stock 1 cup at a time, stir until absorbed. Repeat with the remaining stock and continue cooking until al dente. Fold in the asparagus, corn and peas and season with salt and pepper. Remove from heat and fold in the basil. Serve with Parmesan cheese on the side.
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