For the braised beef filling, preheat the oven to 150C/130C (fan)/Gas 2.
Put all the ingredients in a lidded ovenproof dish and cook for 2-3 hours, or until the beef is very tender. Remove the beef from the dish and shred into small strips. Place in a bowl with a little cooking liquor and set aside.
Put the flour, three eggs and olive oil in a food processor and pulse until it forms small crumbs. Tip the mixture onto a lightly floured work surface and bring together to form a dough. Knead lightly for 2-3 minutes, or until smooth and elastic. Roll into a ball, wrap in cling film and chill in the fridge for 20 minutes.
Lightly flour your pasta machine to prevent the dough from sticking. Take the dough ball from the fridge, and flatten it slightly with a rolling pin, then starting at the lowest (thickest) setting, feed the dough through the machine, turning the handle with one hand and holding the dough as it comes through the machine with the other.
Change the setting on the pasta machine to the next-thickest setting, flour it again and feed the pasta sheet through the machine again, as before. Repeat this process, flouring the machine and changing the setting down each time, until you reach the thinnest setting. You can cut the pasta into smaller individual sheets and work on them individually, keeping the remaining unused dough covered under cling film to prevent it drying out.
Beat the remaining egg in a bowl. Cut out circles from the pasta sheets using a 6cm/2½in pastry cutter, then brush each circle with the beaten egg. Place a heaped teaspoon of the beef filling onto one half of the circle, then fold over the other half and press together to seal. Bring the two corners together to create a ring and pinch to seal. Repeat with the remaining pasta and filling mixture, placing the completed tortellini on a tray lined with greaseproof paper. Cover with cling film until ready to cook.
For the mushroom sauce, heat the butter in a large frying pan until foaming. Add the garlic and cook for 2-3 minutes. Add the mushrooms and cook for 3-4 minutes, or until golden-brown and the liquid from the mushrooms has been released. Pour in the Madeira and cook until the volume of liquid has reduced by half, then add the stock and reduce again by half. Stir in the cream and tarragon and simmer for 5-7 minutes.
To cook the tortellini, bring a large pan of salted water to the boil, add the tortellini and cook for 1-2 minutes or until they float to the surface then remove with a slotted spoon and drain.
Place the tortellini in a serving bowl and pour over the sauce. Garnish with fresh chervil.