Place the tomatoes in an ovenproof dish, pour over the oil and roast in a preheated oven, 200°C (400°F), Gas Mark 6, for 15 minutes. Remove the tomatoes with a slotted spoon, reserving the oil. Peel off the skins and chop to a pulp.
Tip the tomatoes into a heavy-based saucepan with the tomato purée and 1 tablespoon of the roasting oil and cook over a high heat until bubbling. Stir in the honey, cinnamon and ginger and cook for a further 5–10 minutes until the mixture is thick, adding more of the oil if necessary.
Meanwhile, dry-fry the sesame seeds in a small, heavy-based frying pan over a medium heat for 2–3 minutes until golden brown.
Season the jam, tip it into a serving bowl and sprinkle over the toasted sesame seeds. Serve warm or at room temperature with crusty bread for dipping.