In a heavy-bottomed 5- to 6-quart pot, heat 2 tablespoons oil over medium-high heat. Add half of sliced steak to pot in a single layer and cook until well browned, about 2 minutes per side. Transfer steak to a plate. Pour off any oil in pot and repeat with 2 tablespoons oil and remaining steak.
In the same pot, heat 1 tablespoon oil over medium-high heat. Add quartered onion, half of green pepper, and half of yellow pepper. Cook, stirring frequently, until vegetables are lightly browned, about 5 minutes.
Add chicken broth, bay leaves, peppercorns, cumin, and 1/2 teaspoon salt. Add cooked steak and any juices on the plate. The steak should be just covered with broth; pour in additional broth if necessary. Bring to a boil; reduce heat to low and simmer, covered, until steak is fork-tender, 2 1/4 to 2 1/2 hours. Remove pot from heat and let steak cool in broth for 30 minutes.
Transfer steak to a plate. Strain cooking liquid through a sieve set over a bowl; discard solids. Let liquid stand 5 minutes, then skim off and discard any fat. Set cooking liquid aside. Shred steak.
In the same pot, heat 2 tablespoons oil over medium heat. Add thinly sliced onions, remaining green and yellow peppers, red pepper, garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Cook, stirring frequently, until onions and peppers soften, 15 to 20 minutes.
Stir in tomato paste until vegetables are coated. Stir in crushed tomatoes with their juice, 2 1/2 cups of the reserved cooking liquid, and 1/4 teaspoon salt. Bring to a boil; reduce heat to low and simmer until slightly thickened, about 20 minutes.
Return shredded steak to stew and cook until heated through, stirring occasionally, about 2 minutes. Stir in olives. Taste and adjust seasoning with additional salt and pepper if necessary. If not serving immediately, cool, cover, and refrigerate for up to 2 days; flavor will only improve upon standing. Serve with black beans and white rice, boiled potatoes, or fried plantains.