Heat 1 tablespoon olive oil in a large cast-iron skillet over medium-high heat. Season the avocado halves with salt and pepper. Add to the skillet, cut side down, and cook for 5 minutes. Gently flip over and cook for an additional 2-3 minutes. Remove from the skillet and transfer to a warm plate. Lower the heat to medium-low, add the dill to the skillet and cook for 1 minute, stirring. Remove from the heat and set aside in a warm place.