For the consommé, mix the beef mince, carrots, leek and thyme in a large saucepan.
Whisk the egg whites in a small, clean bowl until foamy, then add them to the saucepan and mix in well. Stir in a little of the stock until well combined, then add the remaining stock and stir again.
Heat the pan until the mixture is simmering gently, then continue to simmer for about 1½ hours, without stirring. During this time, the egg whites will rise to the surface of the consommé and take any impurities with it.
Strain the pan contents through a fine sieve lined with a muslin cloth and collect the strained liquid in a clean saucepan (the strained meat and vegetables are not used in this recipe but can be used in another recipe such as a pie or stew). Keep the strained consommé warm.
Meanwhile, for the tortellini, in a large bowl, mix together the flour, egg yolks, and whole egg mixed with water. Rub the dry ingredients into the wet ingredients until the mixture resembles breadcrumbs, then bring the mixture together to form a dough. Alternatively, use a food processor to blend the ingredients together.
Turn out the tortellini dough onto a lightly floured work surface and knead lightly for 2-3 minutes, or until smooth and elastic. Wrap the dough in cling film and chill in the fridge for 20 minutes. Cut the chilled pasta dough into quarters. Roll out one quarter of the dough onto a lightly floured work surface until very thin. This can be done using a rolling pin or a pasta machine. If using a pasta machine, dust the rollers and set them to their widest setting, then pass the pasta dough through the machine, collecting the rolled pasta at the other end. Keep rolling the pasta sheet through the machine, reducing the rollers to their next-widest setting each time, until the pasta has been rolled through the rollers set to their narrowest setting.
Roll out another quarter of the pasta dough in the same way.
Lay one pasta sheet onto a lightly floured work surface. Spoon teaspoonfuls of the pâté at 5cm/2in intervals down one half of the pasta sheet, then spoon another row of pâté portions down the other half to create 2 rows.
Brush the exposed parts of the pasta sheet with the beaten egg, then carefully place the second pasta sheet on top and press down around the pâté filling to seal, pushing out any air bubbles as you go.
Using a cookie cutter, cut discs from the pasta so that the tortellini filling is in the centre of each circle with a 0.5cm/¼in border around it.
Carefully fold the filled pasta discs in half, then twist each end and bring the points over the filling until they meet, so that the filled pasta forms a ring shape.
Repeat the whole process until all of the pâté has been used up and all of the pasta shapes have been turned into tortellini. The remaining unrolled pasta can be frozen for use in another recipe (see tip).
Ball the carrot and the courgette using a melon baller, parisienne scoop or similar (alternatively, dice the carrot and courgette).
Bring a saucepan of water to a simmer and lower the tortellini and carrot and courgette balls into the water. Simmer for 1-2 minutes, then remove from the pan using a slotted spoon and divide equally among serving bowls. Ladle the consommé into the bowls and serve immediately.