To make the dough, put the flour and salt in a stand mixer with a dough hook. Add the egg and oil, then mix on a low speed. Gradually add about 2 tbsp water. Once the mixture starts to clump, tip out onto a lightly floured work surface and knead for about 10 mins until you have a firm, smooth dough. Cut into four portions, wrap each one and rest in the fridge for 30 mins.
To make the filling, combine all the ingredients with some salt and mix well by hand. Fry a small amount to check the seasoning.
Feed one piece of dough through the largest setting on a pasta machine, then fold in half before rolling again. Continue until you reach setting 2/3. Lay the dough out on a work surface dusted with semolina and cut into squares about 6 x 6cm. Spoon 1 tsp of the filling into the centre of each. Brush a little water around the edges and gather up in the centre to form a manti shape (see top image). Continue until you run out of filling, putting the finished manti on a tray heavily dusted with semolina. Keep the remaining pasta wrapped as you work. You’ll have more than you need (see tip, below). Chill the manti for up to 24 hrs.
To make the tomato-chilli butter, melt half the butter in a pan, add the oregano and tomato purée and cook briefly before pouring in the passata with a pinch of salt. Cook over a low heat for around 20 mins. Finish with a splash of sherry vinegar and a pinch of caster sugar. Heat the remaining butter until it browns, pour through a fine sieve, leave to cool for 2 mins, then add the pul biber. Combine the sauce and chilli butter and keep warm. Make the garlic yogurt by whisking the ingredients with 2 tbsp water.
Cook the manti in boiling water for about 5 mins until tender and the meat is cooked though. Drain and serve the manti with the yogurt sauce and chilli butter, and sprinkle with pine nuts and thyme.