Place 1 ½ pounds boneless, skinless chicken breasts on cutting board. Using sharp chef's knife, cut chicken breasts into long strips approximately ½-inch wide. Note: if chicken breasts are especially thick, slice breasts in half horizontally first to create thin cutlets, then slice cutlets into strips.
Once all chicken breasts have been sliced into strips, pat strips of chicken dry on all sides with paper towels. Generously season all sides of each strip of chicken with salt and freshly ground black pepper. Set chicken aside.
Place large skillet on stovetop over medium-high heat. When skillet is warm, add 1 tablespoon olive oil. Heat oil, swirling and tilting pan occasionally to distribute oil across entire surface, until oil is hot and shimmery.
When oil is ready, add seasoned strips of chicken to skillet. Work in batches as needed to avoid overcrowding skillet.
Cook chicken 2 to 3 minutes, then flip chicken over and cook 2 to 3 minutes more, or until chicken is opaque on both sides.
Transfer sauteed chicken to large plate or bowl and set aside. Repeat process with any remaining uncooked strips of chicken.
Once all chicken has been cooked, add 1 tablespoon olive oil to skillet. Heat skillet over medium-high heat, swirling and tilting pan occasionally to distribute oil across surface.
When oil is hot and shimmery, reduce heat under skillet to medium. Add 1 cup thinly sliced white onion, 1 ½ cups thinly sliced green bell pepper, 1 ½ cups thinly sliced red bell pepper, and 2 tablespoons minced jalapeño pepper to skillet and stir to incorporate.
Sauté vegetables, stirring frequently, 7 to 8 minutes or until vegetables are tender.
Once tender, add 3 cloves garlic. Stir to incorporate then sauté until garlic is just fragrant, approximately 30 to 60 seconds.
Pour 1 cup low-sodium chicken broth into skillet and stir to incorporate, scraping bottom of skillet with spoon or spatula to loosen any browned bits of food that may have stuck to pan.
Add ½ teaspoon cumin, ½ teaspoon chili powder, 1 ½ cups canned crushed tomatoes, salt, and freshly ground black pepper to skillet. Stir to incorporate, then increase heat to medium-high and bring mixture to gentle boil.
Once boiling, reduce heat under skillet to medium. Simmer sauce 12 to 15 minutes or until liquid has reduced and sauce has thickened.
When sauce has thickened, return strips of chicken to skillet. Stir to incorporate then simmer chicken in sauce 5 minutes or until strips are cooked through completely.
Remove skillet from heat. Add 2 tablespoons lime juice and 1 tablespoon chopped fresh cilantro and stir to incorporate.
Divide chicken ranchero into preferred portion sizes and transfer to serving bowls or plates. Serve immediately with shredded cheese, sour cream, tostadas, and/or cooked rice as desired.