1cupfreshly grated queso anejo, Parmigiano-Reggiano, or Romano
Heat the butter and oil in a large, deep 12-inch skillet over medium heat. Add the onions and stir to coat; cook for about 12 minutes, stirring occasionally, until they are translucent and the edges begin to brown. Add the garlic and jalapeño or serrano pepper; cook for 2-3 minutes, until softened. Add all of the sliced mushrooms; sprinkle with salt and pepper, and gently combine with the onions. Cover and cook for 5 to 6 minutes, until the mushrooms have exuded their juices and the flavors have melded. Uncover and cook for 7 to 8 minutes or until the juices have evaporated.
Add the cilantro and parsley, stirring to combine. Add the cream and the crumbled queso fresco or farmer cheese; stir until the mixture is thoroughly combined and the cheese has melted. Continue cooking for 3 to 4 minutes, adjusting the heat to keep the mixture barely bubbling at the edges. It should still be very saucy. Turn off the heat.
Preheat the oven to 375°F. Use a little butter to grease a 9-by-13-inch baking dish or the equivalent.
Spoon the cooked rice into the baking dish and level it out without pressing down hard. Pour the mushroom-cilantro mixture on top and gently spread to level it. Sprinkle with the grated cheese. Bake for 15 to 20 minutes or until the cheese has melted and gently browned.