Discard blemished outer leaves of cabbage and carefully peel off the leaves. Tear the leaves by hand into large pieces, about 3 inches wide. If using Napa cabbage, break bottom section of stalks in half vertically to make manageable pieces. Use most of a small head of cabbage, or as much as will fit in your wok.
Heat wok over a high flame until very hot, then lower heat to medium and add the lard and rapeseed oil (or a neutral cooking oil). Add sausage slices and stir-fry until pink disappears. Add garlic cloves, and move them around to insure they do not burn. Cook briefly, then add the chilies and Sichuan pepper. Allow aromatics to become fragrant, but do not brown.
Add the cabbage and stir-fry, turning the contents from bottom to top with a wok spatula until the pieces begin to shrink a bit. They will mostly fill the wok at first, but will shrink after about a minute.
Add the chicken broth to the wok and continue to flip the cabbage. Taste for salt, and add if needed. Cover wok with a lid and steam cabbage for about 2 minutes. When cabbage is done to your liking, stir in cornstarch slurry to thicken the sauce. Plate and serve warm.