Set an oven rack 6 inches from the top element and turn the broiler to high.
Heat a cast iron skillet to medium heat, cook the bacon lardons in the olive oil, stirring occasionally, until the bacon renders much of its fat and starts to brown, about 5 minutes. Reserve 2 Tbs. of the bacon fat in the skillet and set aside.
Add the garlic to the bacon in the skillet. Cook, stirring, until the garlic starts to sizzle, about 30 seconds. Raise the heat to high, add the kale, and sauté, stirring, until it starts to wilt, about 1 minute. Add the chicken broth and beans and bring to a boil. Reduce the heat to medium, cover the skillet, and cook for 5 minutes. Remove from the heat and keep warm.
While the beans are cooking, line a heavy-duty rimmed baking sheet with foil and arrange the salmon, skin side down, on it. Drizzle the reserved bacon fat over the salmon and season with 1/2 tsp. salt and a few generous grinds of black pepper. Broil until slightly firm to the touch, 7 to 10 minutes for medium (the salmon will be dark pink in the middle). Sprinkle half of the thyme over the salmon. Stir the remaining thyme into the beans and kale and season with salt and pepper to taste.
To serve, spoon equal portions of the beans and kale onto dinner plates and top each with the salmon. Serve immediately.