Preheat oven to 375° Fahrenheit.
Place 4 large boneless, skinless chicken breasts on cutting board. Trim chicken as needed. If chicken breasts are unevenly sized or especially thick, pound chicken breasts with rolling pin or meat pounder as needed until all chicken breasts are equal in size and thickness.
Season chicken breasts generously on all sides with salt and freshly ground black pepper to taste. Set chicken aside.
Place large cast-iron skillet on stovetop over medium heat. When pan is warm, add 2 tablespoons avocado oil and continue heating pan until oil is hot and shimmery.
When oil is hot, place seasoned chicken breasts in skillet. Sear chicken 3 to 4 minutes or until opaque, then flip chicken over and sear on other side 3 minutes. Note: if chicken begins to smoke, burn, or stick to pan, add more oil as needed.
Once chicken is opaque on both sides, transfer chicken to large plate and set aside. Return skillet to medium heat. Do not drain or wipe out skillet.
Add 1 ½ tablespoons minced fresh garlic to pan. Stir to incorporate then sauté garlic approximately 60 seconds or until fragrant.
When garlic is fragrant, add ½ cup chicken broth and stir to incorporate, scraping bottom of pan to loosen any bits of chicken or garlic that may have stuck to skillet.
After deglazing pan, remove pan from heat and let cool slightly. Add 1 cup unsweetened, full-fat coconut milk, 2 tablespoons nutritional yeast, ½ cup sun-dried tomatoes, 1 teaspoon dried oregano, ½-1 teaspoon salt, and ¼ teaspoon crushed red pepper flakes. Stir until all ingredients are fully incorporated, then return skillet to heat.
Bring mixture to simmer, then return chicken breasts to skillet. Quickly flip chicken 2 to 3 times to coat in sauce.
Place skillet in preheated oven. Bake chicken 15 minutes, then check internal temperature with meat thermometer. Continue baking as long as needed, checking internal temperature regularly until thermometer reads 160° Fahrenheit.
Once chicken reaches 160° Fahrenheit internally, carefully remove skillet from oven. Set skillet aside and let chicken rest 5 minutes.
After 5 minutes, transfer chicken to serving plates. Spoon sauce from skillet over chicken as desired, then garnish with 2 tablespoons fresh basil and serve immediately with desired sides.