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To make the chicken sauce, heat the oil in a large saucepan over a medium heat and tip in the chicken. Cook for about 5 mins on each side until golden, then lift onto a plate. Tip the onions into the pan and fry for 10 mins until golden. Add the garlic and herbs. Tip the chicken back in, along with the tomatoes and ketchup, then swill a little water around the cans and pour this in, too. Season and bring to a simmer. Cook for 35 mins until the chicken is pull-apart tender and the sauce is thick. Use two forks to shred the chicken into the sauce. Set aside.
Meanwhile, make the white sauce. Put everything in a saucepan with some seasoning, then bring to a simmer, whisking continuously. Simmer for 5 mins, still whisking until smooth and thick, then remove from the heat. If not assembling the lasagne straightaway, cover and set aside to cool before chilling. Will keep covered and chilled for two days.
Spread a thin layer of the chicken sauce in an ovenproof baking dish (ours was 20 x 30cm), drizzle with some of the white sauce and dot over a third of the pesto using a teaspoon. Scatter with a third of the mozzarella, then add a layer of four or five lasagne sheets (you may need to break one of the sheets to fill the gaps), then repeat the layers twice, finishing with a thick layer of the white sauce. Scatter the parmesan over the top. Will keep chilled for a day or frozen for three months. Leave to cool first. Defrost in the fridge overnight before cooking.
Heat the oven to 200C/180C fan/gas 6. Cook for 30-35 mins until browned and crisp around the edges. Leave to stand for 10 mins. Scatter with the basil leaves, grind over some black pepper, then cut into squares. Serve with a crisp green salad, if you like.