For the pâté, saute the shallots in the oil in a frying pan over medium heat until almost translucent. Add the garlic and cook gently for 2 minutes. Add the mushrooms and cook for 5 minutes.
Put the chestnuts, tahini and chickpeas in a food processor and pulse a couple of times. Add the mushroom mixture and process until smooth. Add the tarragon, salt and pepper.
Place the pâté in a plastic or glass container and press down with a spatula, levelling out the top. Place in the refrigerator until ready to use. (This keeps for a few days in the refrigerator.)
Preheat the oven to 180°C (350°F). For the breadsticks, mix the flour, baking powder, salt and sugar in a bowl and make a well in the centre. Pour in the milk and mix to a fairly stiff dough. Divide the mixture into 12 and roll each piece into long cylinders.
Place the butter and olive oil in an ovenproof dish and heat in the oven for a couple of minutes to melt the butter. Roll the breadsticks in the butter and oil. Sprinkle with seeds or dukkah, or make a few of each.
Bake for 15–20 minutes until golden brown. Serve the pâté with the breadsticks. Store the breadsticks in an airtight container for 2–3 days.