Grind the meat through the finest plate of your grinder, running it twice if needed for an extra-smooth texture.
Add the seasonings, eggs, and cornstarch, then mix thoroughly.
Bring the milk to a boil, add the chopped onions, shallots, and carrots, then stir in the bouquet garni, leek greens, parsley, and cloves. Reduce the heat and let the mixture simmer gently for 20 minutes to infuse.
Strain the milk through a chinois and let it cool to about 60 °C before folding it into the meat mixture.
Pour in the Port wine and mix until evenly combined.
Stuff the mixture into the casings, forming even sausages.
Heat a stockpot of water to 90 °C.
Gently lower the sausages into the water, allow the temperature to drop to about 78 °C, and poach for 20–30 minutes.
Lift the sausages out of the water and plunge them into cold water to halt the cooking.
Hang the sausages to drain thoroughly.