In large bowl, whisk together cornmeal and water. In 3-quart saucepan, bring stock and oil to boil. Whisk in cornmeal and stir until mixture thickens, about 3 or 4 minutes. That will keep polenta smooth and free of lumps.
Cook over medium heat, stirring constantly with wooden spoon, 25 minutes.
Add cheese; mix well. Cover pot and leave on heat 3 minutes, without stirring. Shake pot a little to allow some steam to get under polenta so it will unmold from pot easily.
Coat 8 1/2 x 4 1/2 inch loaf pan with nonstick spray. Add polenta and allow to set until quite firm.
Unmold it onto cutting board or countertop. Cut into 3/4 to 1 inch slices.
saute, broil or bake slices until hot; add asparagus topping.
Steam asparagus until tender, about 5 to 7 minutes. In large frying pan, combine mushrooms, shallots, stock and oil. Cook over medium heat until mushrooms are tender. Stir in chives, tarragon and asparagus. Heat through. Sprinkle with cheese.