In a 5- to 6-quart pan, combine mushrooms, poblano chilies, onion, cumin seeds, and 1/2 cup broth. Bring to a simmer over medium-high heat; cover, reduce heat, and simmer until vegetables are juicy and limp, 12 to 15 minutes. Uncover, increase heat to high, and stir often until vegetables are dry and beginning to brown, about 20 minutes.
In a bowl, blend cornstarch with the remaining 1 cup broth. Add 1/2 cup sour cream and whisk to blend. Add to mushroom mixture and stir until boiling, 1 to 3 minutes.
In a blender, whirl beans, salsa, and enchilada sauce.
Pour 1 1/2 cups bean sauce into a 9- by 13-inch baking dish. Stack 6 tortillas and cut in half. Lay 6 of the halves in casserole, straight edges against casserole sides, then overlap 3 whole tortillas to completely cover bottom. Scrape mushroom mixture onto tortillas and spread level. Fit straight edges of remaining tortilla halves against casserole sides, then overlap remaining whole tortillas to cover filling. Pour remaining black bean sauce over tortillas and spread to coat completely.
Bake in a 350° oven until sauce is bubbling, 35 to 40 minutes (45 minutes if chilled). Sprinkle with cheese and bake until melted, 3 to 5 minutes longer.
Remove casserole from oven and let stand 10 to 15 minutes. Top decoratively with cucumbers, if desired, and cilantro. Scatter about half the vinegared red onions over casserole; put remaining in a small bowl. Spoon remaining sour cream into a bowl.
With a sharp knife, cut enchilada casserole into 6 or 9 rectangles; with a wide spatula, transfer portions to plates. Add more sour cream and vinegared onions to taste.
Vinegared red onions: Peel and thinly slice 1 red onion (8 oz.). Separate rings and drop into a 10- to 12-inch frying pan. Add 3/4 cup seasoned rice vinegar and bring to a boil over high heat, stirring occasionally, 2 to 3 minutes. Remove from heat and let stand until cool, stirring often. Serve, or cover and chill for up to 3 days. Lift from liquid to use. Makes about 1 cup.
Do-Ahead Tip: You can make the filling (steps 1 and 2) and sauce (step 3) up to 1 day ahead; cover separately and chill. You can assemble the casserole (through step 4) up to 2 hours ahead; cover and chill.