1
Bring stock to a simmer in a medium saucepan. Add asparagus trimmings and simmer until mushy. Remove asparagus and return to simmer.
2
Heat 2 tablespoons oil over medium heat in another saucepan. Cook onion, stirring frequently, until soft, 6 to 7 minutes. Add rice, cook, stirring, until edges are translucent, 2 to 3 minutes. Add wine; cook, stirring, just until evaporated.
3
Add 1/2 cup hot stock; cook, stirring, until almost absorbed. Continue adding 1/2 cup stock in this manner until liquid is creamy and rice is al dente, about 20 minutes total (you may not need to add all the stock). Add asparagus with the last addition of stock, and the eggplant about 1 minute before risotto is done.
4
Remove from heat; stir in parsley and cheese. Season with salt and pepper. Serve immediately with additional cheese.
