Place all the ketchup ingredients into a small, heavy-based frying pan and bring to the boil. Reduce the heat and gently simmer for 5–7 minutes, uncovered, stirring occasionally until the sauce is thick and pulpy. Whiz in a food processor until smooth, then place in a jar and cool. (Store in a refrigerator for up to 2 weeks.)
Cut along the length of each sausage, ease the skin off and discard it. Place the sausagemeat in a bowl with the herbs and honey and mix well. Using damp hands, shape into 8 small patties, then cook under a preheated medium grill for 10–12 minutes, turning once, until golden.
Meanwhile, bring a frying pan half-filled with water, with the vinegar added, to the boil. Reduce the heat to a simmer, then immediately break the eggs, well spaced apart, into the water and cook for 1 minute until the white is opaque. Remove from the water using a slotted spoon and keep warm.
Toast the muffin halves until golden and lightly crisp. Place a warm muffin half on to each of 4 serving plates and top with 2 sausage patties, a poached egg and a spoonful of ketchup.