Position a rack in the center of the oven and preheat to 450 degrees. Mix the first 4 Spice Blend ingredients; season with salt and pepper.
In a baking dish, drizzle the chicken or fish with olive oil, then rub with the Spice Blend. Top each piece with a shingled layer of the tomatoes and onion. Scatter with the garlic and jalapenos; drizzle with olive oil. Roast until cooked through (20 minutes for chicken; 15 minutes for fish). Top with the queso fresco and cilantro.
Dress the avocados with the lime juice; season. Toss with the romaine; drizzle with the EVOO. Serve with the chicken or fish.