Heat the oil in a large, heavy-based frying pan, then cook the bacon over a moderate heat for 2–3 minutes until beginning to turn pale golden. Add the carrot and cook for 1 minute more.
Add the tomatoes, tomato purée and honey and heat until the tomato juice is bubbling. Add the beans, then reduce the heat and simmer for 4 minutes, uncovered, until the tomato juice has reduced and thickened slightly. Stir in the parsley, if liked, and set aside.
Lightly toast the bread under a grill until golden and just crisp. Place on warmed serving plates and pile the herby beans and bacon on top. Sprinkle with the Parmesan, if liked.