Heat 2 Tbsp olive oil in a large skillet over medium-high heat until it begins to shimmer, add the chuck roast and brown 3–4 minutes per side. When the roast is browned on both sides, transfer it to the slow cooker.
Add additional 2 Tbsp olive oil to the skillet and add onion. Cook 3–4 minutes, scraping up any brown bits that are stuck to the bottom of the skillet. Add garlic, cook 1 additional minute then add tomato paste, chili powder, oregano, red pepper flakes, and cumin. Stir into a paste, cook approximately 30 seconds to toast the spices then add the diced tomatoes, beef bouillon and chicken broth. Bring to a boil, remove from heat then pour over the roast.
Cover and cook on low heat 8–9 hours or 5–6 hours on high heat until it falls apart when pierced with a fork.
Remove the meat from sauce, shred it into ¼–½" pieces then place it into a large bowl and cover with aluminum foil to keep warm. Remove fat from the top of the sauce. Add just enough sauce to the shredded beef to moisten it. Reserve remaining sauce to serve on the side of the quesadillas.
Place black beans in a glass bowl, cover with a paper towel then warm in the microwave for 2 minutes. Set aside.
Place a skillet over medium heat and brush a small amount of butter or oil onto the bottom of the pan. Place a tortilla into the skillet then immediately add ¼ cup shredded cheese to cover one half of the tortilla. Spread roughly ¼ cup of shredded beef on top of the cheese then add about 1 tsp green chilies and 3 Tbsp black beans over the meat. Fold the uncovered half of tortilla on top of the side with the filling.
Press down on the quesadilla with a spatula to seal the top and bottom together with the filling. Allow the tortilla to cook 2–3 minutes on the first side until golden brown and crispy.
Flip the quesadilla and repeat for the opposite side. If the tortilla becomes too brown before the cheese melts, lower the temperature. The objective is for the cheese to be completely melted and gooey at the same time the tortilla becomes golden and crispy. Generally, if you have the patience for it, lower heat is better.
Transfer the quesadilla to a cutting board, cut into wedges then serve with reserved sauce, sour cream and chopped cilantro. Plain white rice makes a nice side to this flavorful dish.
One Last Thing
Combine any remaining meat with a bit more sauce and store in the freezer for up to one month for on-the-fly burritos or tacos.