1. Remove and discard sausage casings. Crumble meat in a 12- to 14-inch frying pan over medium-high heat. Add garlic, cumin, and oregano. Stir often until sausage is lightly browned, 8 to 10 minutes. Drain and discard fat.
2. Meanwhile, trim and discard discolored mushroom stem ends. Chop mushrooms. Add to sausage mixture. Squeeze moisture from spinach and add to sausage mixture. Stir often over high heat until mixture begins to brown, about 10 minutes longer. Remove from heat. Stir in bread crumbs and cheese. Season to taste with salt. Add egg and mix well.
3. Rinse and drain chilies. From stem to tip, cut each chili open lengthwise. Ease open chili and carefully pull out and discard seeds and veins. Fill chilies equally with chorizo stuffing, packing it in firmly. Lay chilies, slit side up, in a single layer in a 10- by 15-inch pan.
4. Bake in a 400° oven until chilies are soft and tinged with brown, about 25 minutes. With a wide spatula, transfer to a platter.