Warm a large skillet over medium-high heat, add the avocado oil, then add the chicken and season it with the garlic, dried basil, kosher salt, pepper, and oregano. Cook, stirring occasionally, until the chicken is browned and reaches 165°F in the thickest pieces; transfer it to a plate.

Lower the heat to medium and pour the heavy whipping cream into the same skillet. Scrape up the browned bits as the cream forms small, steady bubbles around the edges.

Stir in the shredded parmesan, then take the skillet off the burner and whisk until smooth. The sauce should coat the back of a spoon in an even layer rather than immediately running off.

Return the cooked chicken to the skillet and fold it through the sauce until coated. Finish with fresh chopped parsley for garnish when the sauce looks glossy and velvety.