Gather all ingredients. In a bowl, combine the melted butter, red wine vinegar, chicken broth, tomato paste, yellow mustard, grain mustard, liquid smoke, soy sauce, chili powder, cumin, cayenne pepper, erythritol, and fish sauce.

Stir the sauce until combined. Taste the sauce, adding more vinegar for added tang and more erythritol for added sweetness as needed. Note: the flavor of the sauce will change some as it blends with the chicken juices during cooking.

Add the chicken thighs to a slow cooker. Turn the slow cooker on to low and measure out the butter on a plate, letting it sit to come to room temperature. After 2 hours, there should be quite a lot of juice from the chicken in the slow cooker. Submerge the chicken thighs in the juice.

Pour the sauce over the chicken and add the butter. Turn the slow cooker to high and let cook for an additional 3–4 hours. Alternatively, if you will be out all day, simply put the chicken, sauce, and butter in the slow cooker and cook on low for 7 hrs. Shred the chicken until no large pieces remain. Keep (or set) the slow cooker on high and remove the lid, cooking for an additional 45 minutes to reduce sauce.

After 45 minutes, the sauce should have reduced by about an inch. Mix the chicken into the sauce and serve.