Pat the chicken tenderloins completely dry with a paper towel. Moisture on the surface prevents a proper sear.

On a shallow plate, combine the flour, dried basil, salt, pepper, cayenne, garlic powder, and onion powder. Stir to mix evenly. Dredge each tenderloin through the mixture, pressing gently so it sticks, then shake off any excess.

Heat a large skillet over medium-high heat. Add the butter and oil and swirl to coat. Wait until the butter is fully melted and the pan looks shimmery before adding the chicken.

Add about half the chicken tenderloins in a single layer, leaving about an inch between each piece. Sear for 4 minutes without moving. Reduce to medium if the pan smokes too much. Flip and cook another 2 minutes until golden brown.

Transfer the first batch to a plate. Repeat with the remaining tenderloins, adding more oil if the pan is dry. Set all cooked chicken aside.

With the heat on medium-high, pour in the chicken broth and lemon juice. Scrape up all the browned bits from the bottom with a wooden spoon. Bring to a boil and simmer for 3 minutes.

Pour in the heavy cream and stir to combine. Bring back to a gentle simmer and cook for 5 to 8 minutes, stirring occasionally, until the sauce thickens enough to coat the back of a spoon.

Remove the pan from heat completely. Stir in the fresh basil and lemon zest off the heat to keep the basil bright green. Return the chicken to the pan, spoon the sauce over the top, and serve immediately over pasta, rice, or mashed potatoes.