In a large skillet, heat olive oil over medium-high heat. Season the beef chuck roast with salt, pepper, garlic powder, onion powder, cumin, and chili powder. Sear the roast on all sides until browned, about 4-5 minutes per side.
Transfer the seared roast to a slow cooker. Pour in the beef broth and diced tomatoes with green chilies. Cover and cook on low for 8 hours or high for 4 hours, until the beef is tender and easily shredded.
Once cooked, remove the beef from the slow cooker and shred it using two forks. Return the shredded beef to the slow cooker and mix it with the juices.
Preheat your oven to 350°F.
To assemble the enchiladas, spoon a portion of the shredded beef mixture onto each tortilla, sprinkle with cheese, and roll them up tightly. Place the rolled tortillas seam-side down in a greased 9x13 inch baking dish.
Pour the enchilada sauce over the top of the rolled tortillas and sprinkle with the remaining cheese.
Bake in the preheated oven for 20-25 minutes, until the cheese is melted and bubbly.
Remove from the oven and let cool for a few minutes. Garnish with chopped cilantro if desired and serve with sour cream on the side.