Preheat your oven to 375°F. In a large 7-quart Dutch oven, add the beef consommé, olive oil, light brown sugar, and honey Dijon mustard. Use a whisk to mix everything together until combined.
Add the smoked paprika, garlic powder, onion powder, salt, lemon & pepper seasoning, and chili powder to the pot. Mix well until the spices are fully incorporated into the liquid.
Nestle the chicken breasts into the liquid mixture. Use a fork to poke each piece 3–4 times — this helps the sauce penetrate into the meat as it cooks. Place the lid on the Dutch oven and transfer it to the preheated oven. Cook for 45 minutes, or until the internal temperature of the thickest chicken breast reaches 165°F.
Remove the Dutch oven from the oven and increase the oven temperature to 400°F. Using two forks, shred the chicken breasts. It can be easier to lift the chicken onto a plate or cutting board for shredding, then return it to the Dutch oven.
Place the shredded chicken back into the Dutch oven and stir well so every piece is coated in the sauce. Return the Dutch oven to the oven, this time uncovered, and cook for an additional 10–15 minutes.
After 10–15 minutes, mix the chicken again and broil for 5 minutes if you'd like slightly crispy edges. Keep an eye on it so it doesn't burn.
Notes
Check the temperature, not the clock. Oven temperatures vary, so use a meat thermometer to confirm the chicken has reached 165°F internally before shredding — this is the most reliable way to know it's done.
Poking the chicken matters. Those fork holes allow the braising liquid to seep into the meat during cooking, not just coat the outside. Don't skip this step.
Shred on a plate or cutting board. It's much easier to shred the chicken when it's not submerged in liquid. Pull it out, shred it, then toss it back in the sauce.
Let it soak. If time allows, let the shredded chicken sit in the sauce for a few extra minutes before serving. The more it soaks, the more flavorful every bite will be.
Broil for texture. The optional broil step in the last 5 minutes adds a slightly caramelized, crispy texture to the top of the chicken that takes it to the next level.
Use a Dutch oven with a tight-fitting lid. The seal traps moisture during the first cook phase, which is what keeps the chicken juicy and tender. A loose lid can let too much steam escape.