1. For steak: Stir oil, allspice, salt, garlic powder, cayenne, and pepper together in a bowl, to make a paste. Rub mixture all over steak and set aside until room temperature, about 20 to 30 minutes.
2. Preheat a grill to high.
3. For mojo: Toast cumin seeds in a small dry skillet over high heat until fragrant, about 30 seconds. Grind seeds in a spice grinder or using a mortar and pestle.
4. Heat olive oil and garlic along with toasted cumin over medium-high heat until garlic begins to sizzle, about 2 minutes. Cool oil slightly and whisk with lime juice, oregano, salt, pepper, and jalapeno in medium bowl.
5. Grill steak until slightly charred and crisp and medium-rare, about 4 minutes per side.
Set aside on a cutting board and let rest for 10 minutes.
6. Brush plantains lightly with oil and season with salt and pepper. Place on grill, skin-side down, and cook until soft and skin is charred about 5 minutes. Turn and cook to sear on grill marks, about 2 minutes more.
7. Slice steak and arrange on a platter with plantains, drizzle with some mojo. Serve with remaining sauce at table.
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