Bring a small saucepan of salted water to a boil. Add the asparagus tips and cook until tender but still firm to the bite, 1 to 2 minutes, depending on size. Drain asparagus and set aside.
If using fresh peas, cook them in another small saucepan of salted boiling water until tender but still firm to the bite, 5 to 10 minutes, depending on size. Drain peas and set aside. (Asparagus and peas may be cooked several hours ahead.)
Heat the stock in a medium saucepan, and keep warm over low heat.
Heat 3 tablespoons of the butter in a large skillet over medium heat. When the butter foams, add the onion and cook, stirring, until onion begins to color, 3 to 4 minutes. Add the rice and stir until it is well coated with the butter and onion, about 1 minute. Add the wine and stir until it is almost all reduced. Add about 1/2 cup of the hot stock, or just enough to barely cover the rice. Cook, stirring, until the stock has been almost completely absorbed. Continue cooking and stirring the rice in this manner, adding 1/2 cup stock at a time, for about 15 minutes. At this point the rice should be tender but still a bit firm to the bite.
Stir the artichokes, asparagus, and peas into the rice, and season lightly with salt. Add the remaining tablespoon butter and the Parmigiano. Mix quickly for 1 to 2 minutes until the butter and the cheese have melted and the rice has a moist, creamy consistency. Taste and adjust the seasoning; serve immediately with additional cheese sprinkled over the top, if desired.
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