In a small saucepan over medium-high heat, bring the chicken broth to a simmer. Reduce heat to low and cover, keeping the stock hot.
Heat olive oil in a large saucepan over medium-high heat. Add the onion and sauté, stirring frequently for 2 minutes. Add the mushrooms, cook until tender and slightly brown – about 8 minutes. Add garlic and cook for 2 minutes longer. Add the rice, stirring well. Add the white wine and simmer, stirring constantly until the liquid is absorbed – about 2-3 minutes. Add 3/4 cup of the hot chicken broth. Reduce heat to medium and cook, stirring frequently, until the stock is absorbed.
Add the remaining broth 3/4 cup at a time, stirring frequently – allowing each addition to be fully absorbed before adding more, until the rice is just tender and the risotto is creamy.
Stir in the Parmesan cheese, thyme (optional), asparagus (optional), and butter. If the rice appears dry, add up to 1/4 cup water to loosen the risotto slightly. Season with salt and pepper to taste.
Sprinkle parsley over top and serve.