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First, make the buns. Heat the milk and honey in a saucepan until steaming. Add the butter, then set aside to cool. Mix the flour, cumin, yeast and 1 tsp salt in a large bowl. Add the cooled milk mixture and stir to form a dough. Tip the dough onto a work surface and knead for 10 mins until soft and stretchy, or mix with a dough hook in a food mixer for 5 mins. Return to the cleaned bowl, cover with cling film and set aside to rise for 1-2 hrs or until doubled in size.
Meanwhile, heat the oil in a large pan. Add the onion and cook for 5 mins until soft. Add the garlic and chilli, stir for 1-2 mins, then tip in the lamb. Brown the mince all over, breaking it up with a wooden spoon, then add the tomato purée, curry powder and flour and cook for 2-3 mins more. Add the chopped tomatoes and mango chutney along with 150ml water, season well, cover and cook for 30 mins (add some more water if the mince looks too dry).
When the dough has risen, knock out the air and divide into eight equal pieces. Shape into balls by pinching and tucking the edges into the centre, then flip over so the smooth side is on top. Arrange on one or two baking sheets lined with baking parchment. Squash each bun a little with your palm – they should be about 8cm in diameter. Cover loosely with oiled cling film and leave to rise for 30 mins or until almost doubled in size. Heat oven to 200C/180C fan/gas 6.
Check the consistency of the mince – it should be thicker than a ragu. If it’s too runny, remove the lid and continue cooking until the sauce has reduced.
Uncover the rolls, brush with the beaten egg and sprinkle with cumin seeds. Bake for 20-25 mins until golden brown, then transfer to a wire rack and leave to cool. If making a day ahead, store in an airtight container.
To serve, fry the eggs to your liking. Split the buns and lightly toast the cut sides under the grill. Pile in the spicy lamb, fried eggs, coriander, shallot and carrot. Serve with extra mango chutney and tuck in with plenty of napkins to hand.