Pour broth into good sized pot (eventually all ingredients except for tortillas and shredded cheese will end up in it) over med-high to boil. Add chili powder, cumin, garlic, peppercorns, and salt. Meanwhile slice roast into narrow strips across the grain. Add roast to broth, bring to boil, then cover and reduce heat to low. Simmer for 30 min or until meat is flavored and tender. Remove peppercorns and adjust seasoning to taste, if needed.
When meat is done increase heat to med-high and add cubed Velveeta. Drain pinto, black beans, and corn; rinse beans well. Once cheese is melted add beans, corn, and un-drained green chiles. Add oregano and additional cumin/chili powder if wanted (my kids like it mild). Boil for five min or so to mix flavors, then add cornstarch slurry and boil until thickened. Don't worry if it's a bit thin, it'll thicken while baking.
Pre-heat oven to 350. In a greased (or sprayed with non-stick cooking spray) place 1/3 of the tortilla pieces on the bottom of the pan. Sprinkle 3/4 cup cheese, place 1/2 the filling over cheese, and sprinkle 1/2 the cilantro. Repeat with tortilla pieces, 3/4 cup cheese, remainder of filling, and remainder of cilantro. Top with last 1/3 of tortilla pieces and remaining 1-1/2 cup of cheese.
Place in pre-heated oven for 15 minutes, or until cheese has melted. Garnish with extra cilantro, if desired.