Heat a large cast-iron skillet over medium-high heat. Add the cumin seeds and toast, stirring occasionally, about 1 minute; transfer to a bowl. Add the garlic and chiles to the skillet. Cook, turning occasionally, until soft and blackened in spots, about 5 minutes. Transfer to a food processor and let cool. Add the cumin seeds, vegetable oil, 1/4 cup lime juice and the brown sugar and puree until smooth. Season with 1 1/2 teaspoons salt and a few grinds of pepper. Transfer to a resealable plastic bag and add the steak, shaking well to coat. Refrigerate, 1 to 4 hours.
Soak the onion in a bowl of cold water. Meanwhile, wipe out the skillet and heat over high heat. Cook the tomatillos, turning, until well charred, about 7 minutes. Transfer to a plate and let cool. Remove the charred husks and roughly chop the flesh. Drain the onion. Wipe out the food processor; add the tomatillos, onion, cilantro and the remaining 1 to 2 tablespoons lime juice and puree until smooth. Season with 3/4 teaspoon salt and a few grinds of pepper; set aside.
Meanwhile, bring the steak to room temperature, about 30 minutes. Preheat a grill to high. Remove the steak from the marinade and shake off any excess. Lightly oil the grill, then grill the steak until charred on the bottom, about 5 minutes. Flip and cook until charred on the other side, 1 to 3 more minutes. Transfer to a cutting board and let rest 10 minutes.
Warm the tortillas on the grill. Thinly slice the steak against the grain. Double up the tortillas and fill with the steak and tomatillo salsa. Top with cheese and radishes.