Place a large heavy skillet, such as cast-iron, over high heat until very hot. Brush the cut sides of the tomatoes with 1 teaspoon oil and place cut-side down in the pan. Cook until charred and beginning to soften, 4 to 5 minutes. Brush the tops lightly with another 1 teaspoon oil, turn and cook until the skin is charred, 1 to 2 minutes more. Transfer to a plate to cool. Do not clean the pan.