Pollo Picante Con Huevos

Name: Pollo Picante Con Huevos
Ingredients: 1⁄4 cup raw jasmine rice; 1⁄2 teaspoon extra virgin olive oil; 1 small chicken breast, diced; 1⁄2 cup red onion, diced; 2 small garlic cloves, minced; 1⁄4 cup carrot, grated; 1⁄4 cup broccoli, grated; 1 small tomatoes, diced; 1⁄4 cup canned tomato sauce; 1⁄2 teaspoon paprika; 1⁄2 teaspoon cumin; 1⁄2 teaspoon italian seasoning; 1⁄2 teaspoon crushed red pepper flakes; 1⁄2 teaspoon chili powder; 1 cup water, as needed (or more); 2 tablespoons white vinegar; 2 bay leaves; 2 small eggs; 1⁄2 teaspoon salt (to taste); 1⁄2 teaspoon pepper (to taste)