Combine the garlic, both paprikas, olive oil, salt and pepper in a zip-top bag. Add the steaks and marinate overnight or for at least 4 hours.
Soak the ancho chile in water overnight.
Preheat the oven to 400°F.
On a baking sheet, toss the onions, garlic, and tomato for the romesco sauce with 1 tablespoon olive oil and a pinch of salt and pepper. Roast until beginning to caramelize, about 15 minutes. Transfer the roasted vegetables to a blender, along with the almonds, roasted red peppers, sherry vinegar, and honey. Blend until smooth. With the motor running, drizzle in the oil until emulsified. Season to taste with salt and pepper.
In a large pot, cover the potatoes with cold water and bring to a simmer. Simmer until soft but not mushy, about 16 to 20 minutes. Drain the cooked potatoes and return to the saucepan; place over a medium-low heat for 1 to 2 minutes to dry out the moisture, then mash using a potato masher. Quickly fold in the milk, sour cream, butter, and parmesan and season to taste.
On a baking sheet, toss the broccoli with the garlic, oil, salt and pepper. Roast for 12-15 minutes, until crisp tender.
Heat a grill or large skillet to medium-high. Remove the steaks from the marinade, discard the marinade, and grill for 2 to 3 minutes per side to sear. Transfer to a baking sheet and roast to desired doneness, 8 to 10 minutes (for medium-rare the internal temperature should be 135°F, 125°F for rare). Rest for 5 minutes before serving.
To serve, divide the mashed potatoes, broccoli and steak between plates. Serve with romesco on the side.