Cook the bacon. Add the chopped bacon to a large skillet over medium heat until cooked through and the fat has rendered. Transfer the bacon to a paper towel-lined plate, leaving the drippings in the skillet. If there isn't enough fat to lightly coat the bottom of the skillet, add a small drizzle of avocado oil.
Sauté the aromatics and add the cabbage. Add the onion to the bacon drippings and cook for 2–3 minutes, stirring occasionally, until it begins to soften. Add the garlic and cook for about 30 seconds, just until fragrant. Add the cabbage ribbons.
Add the seasonings. Add the thyme, kosher salt, and black pepper. Toss well to coat everything in the bacon fat. Cook over medium to medium-high heat, stirring occasionally, until the cabbage begins to soften and develop lightly browned edges, about 8–10 minutes.
Cook until tender. Add chicken broth to deglaze the bottom of the pan and continue cooking for another 3–5 minutes.
Finish. Stir in the whole-grain mustard and reserved bacon. Taste and adjust the salt and pepper as needed.