The easiest way to make simple grilled shrimp even more flavorful in a matter of minutes? Make a dipping sauce — this one has a nice blend of bright, herbaceous cilantro; spicy chili pepper sauce; and tart lime juice.
Heat the olive oil in a frying pan over medium heat. When it shimmers, add the two pieces of shallot, cut-side-down. As soon as you see bubbles around the shallot halves, turn the heat down as low as it will go. Cook the shallot halves just until they start to brown, about 5 minutes. Remove and discard the shallot and allow the oil to cool to room temperature.
Rinse the shrimp and pat them dry with paper towels. Then, remove the veins from the shrimp. Drizzle 1 tablespoon of the shallot oil over the shrimp, season with salt and pepper, and toss to coat.
Heat your grill (or a cast-iron grill pan) over medium-high heat. Grill the shrimp in the preheated pan just until opaque and nicely charred, about 1–2 minutes per side.
Combine the remaining 3 tablespoons of shallot oil with the wine, chili garlic sauce, lime juice, and cilantro leaves. Pour the sauce over the grilled shrimp or serve it on the side, for dipping.