Heat oven to 375°F. Grease cookie sheet. In small skillet, combine onion, pine nuts and tomatoes; cook and stir over medium heat for 1 to 2 minutes or until onion is tender and nuts are toasted. Remove from heat. Stir in poppy seed.
Unroll dough; separate into 2 sections (6 breadsticks each). Spread onion mixture over dough. Reroll dough sections; pinch edges to seal. Cut each section into 6 rolls. Place rolls cut side up on greased cookie sheet. Brush with reserved 1 tablespoon tomato oil. Sprinkle with cheese.
Bake at 375°F. for 13 to 17 minutes or until golden brown. Serve warm.