In a small bowl toss the arugula with 1 tablespoon each of the olive oil and red wine vinegar. Season with salt. Divide the arugula between 2 serving plates.
Toss the tomatoes with the remaining olive oil, vinegar, oregano, and salt. Arrange the tomatoes on the serving plates.
Spread 1 ounce of goat cheese onto each slice of grilled bread. Serve 2 slices of grilled bread with goat cheese with each plate.