There are several different ways to prepare polenta with these two vegetables. This variation yields a gratin-like dish with rich, caramelized leeks on the bottom, a crispy crust on top, and moist interior. You can easily double this recipe if you have two bunches of asparagus, and use a bigger pan.
Snap the bottoms off 1 bunch of asparagus and then soak in a cold water bath. Drain and cut into bite sized pieces. Slice any extra-fat pieces in half lengthwise. Set the tips of the asparagus aside for now.
In a medium sized pot, bring 3 C. of well-salted water to a boil. Add 1 C. regular (not quick-cooking) polenta and 1 T. butter or olive oil. Low to a simmer and stir frequently until the polenta is thick and no longer crunchy. Taste and season with salt and pepper, then stir in 1 C. grated monterey jack cheese and the asparagus. Allow to cool for at least 20 minutes.
Cut the tops off 1 large or 2 smaller leeks, then slice in half lengthwise and clean well. Cut the leeks into thin matchsticks lengthwise, about 1 inch long. Place the leeks in a 10 inch cast iron skillet or 9″ square pyrex baking dish. Toss with 2 T. olive oil, salt, pepper, and 1/2 t. dried thyme leaves or 1/2 T. fresh. Spread the leek mixture evenly over the bottom of the pan.
Spoon or pour the polenta over the leeks, then use a spatula to smooth the top. Press the reserved asparagus tips down into the polenta shallowly so that you can still see them. Sprinkle another 1/2 C. grated jack cheese over the top.
Bake the polenta in the oven at 375 degrees until it is firm and the top is nicely browned. If necessary, switch the oven to broil for a few minutes before removing.