1. Preheat oven to 475 degrees, with racks in upper and lower thirds. Divide mushrooms, garlic, and 1 tablespoon oil between two large rimmed baking sheets; season with salt and pepper, and toss. Roast, tossing occasionally, until mushrooms are tender and browned, 15 to 20 minutes. Refrigerate 2 cups for Steak Tostadas with Cilantro Sour Cream, up to 2 days. Set aside remaining mushrooms.

2. In a small bowl, combine paprika, oregano, red-pepper flakes, and 2 teaspoons salt. Rub steaks with 1 tablespoon oil, then spice mixture.

3. In a large skillet, heat 1 tablespoon oil over medium-high. Sear steaks in two batches, 5 to 7 minutes per side for medium-rare (lower heat if skillet gets too dark). Transfer steaks to a plate; refrigerate one steak for Tostadas, up to 2 days. Tent remaining steak with aluminum foil to keep warm.

4. In a large bowl, whisk together vinegar and remaining 2 tablespoons oil; season with salt and pepper. Add spinach; toss to combine. Thinly slice steak against the grain; serve with mushrooms and spinach salad.