Everything cold. The meat, the cream, the bowl, the blade, the grated butter. Put the processor bowl in the freezer for ten minutes first if the kitchen is warm.
Combine the salted venison, cream, egg whites, grated butter, rice, shallot, garlic, white pepper, nutmeg and thyme in the food processor. Pulse to a smooth paste, stopping every ten seconds to scrape down and feel the bowl. If the paste climbs past 50°F, put the whole thing in the freezer for ten minutes before carrying on. A warm paste is a broken paste and there is no bringing it back. It is ready when a spoonful holds a soft peak and springs back when you press it.
Stuff into hog casings and tie into 10 links, each about six inches long and no thicker than an inch and a quarter. Or roll into 10 tight logs the same size in a double layer of plastic wrap, twist the ends, tie them off with string and wrap once in foil so no water gets in. Use a wrap or bag whose box says it is safe for cooking or boiling, not one sold only for covering and storing. Chill 30 minutes before poaching. Anything fatter than an inch and a quarter will not cook through in the time below, and anything longer will not fit a bun.
Bring a large pot of lightly salted water to 180°F and hold it there, never letting it bubble. Slide the links in. They are done when the center of the thickest one reads 160°F, about 18 to 25 minutes. There is no way to see this: a boudin blanc is white raw and white cooked, so the thermometer is the only thing telling you the truth. A hard boil bursts casings and squeezes the water out of the paste you just built.
Lift them out, pat dry, and put them in the fridge for 10 minutes before they see a pan. They are fully cooked now, and chilling the outside is what stops them bursting or drying in the butter.
Skillet over medium heat. Butter, and let the foam subside. Sear about 4 minutes in all, turning, until deeply golden all round. Medium, not high: butter burns at 350°F and a hot pan here only squeezes the juice out of a sausage that is already cooked. This is colour, not cooking.