Brush both sides of each slice of sourdough with olive oil. Heat a grill pan over medium-high heat, then grill bread for two minutes on each side, or until charred. Remove to a plate.
Whisk together olive oil, balsamic vinegar, honey, chopped fresh rosemary, salt, and pepper. Pour onto a small plate.
Cut each slice of sourdough into four thick strips and arrange around the plate with oil.