Combine all ingredients except water and vinegar and toss to distribute the seasonings. Chill until ready to grind.
With a meat grinder or Kitchen Aid attachment, grind the mixture through a small die into a mixing bowl set over ice.
Add the water and vinegar to the meat mixture and mix with the paddle attachment or your hands until the liquids are incorporated and the mixture has developed a uniform, sticky appearance, about 1 minute on medium speed in a mixer, or longer with your hands.
Sauté a small portion of the sausage over medium heat, taste, and adjust the seasoning if necessary.
With a sausage stuffer, stuff mixture into pork middles 6 to 8 inches long, pricking the casings with a needle as you go to prevent air bubbles. Twist the casing off into links and let sit overnight in the refrigerator.
To cook, heat oil in a skillet and sear on medium-low heat for about 15 minutes, turning often. The internal temperature should be 160 degrees F.