In a large bowl, combine salt, pepper, garlic powder, onion powder, chili powder, and smoked paprika. Drizzle in olive oil to form a loose paste, then add the chicken tenders and toss to coat evenly. Let stand at room temperature for 10 minutes while you heat the pan.
Set a wide skillet over medium heat. Melt 1 tablespoon of the butter, then add half the chicken in a single layer. Sear until well browned, 3 to 4 minutes per side, adjusting heat to avoid scorching the spices. Transfer to a plate and repeat with remaining chicken, adding a teaspoon of oil if the pan looks dry.
Pour the chicken broth into the hot skillet and scrape up the browned bits. Let it bubble for about 1 minute until reduced by half.
Lower the heat to medium-low. Stir in the heavy cream and 1 tablespoon butter. Simmer gently, stirring occasionally, until the sauce thickens enough to lightly coat a spoon, about 5 to 6 minutes. Taste and adjust salt or pepper if needed.
Return the chicken and any accumulated juices to the skillet, turning to coat. Simmer uncovered for 2 minutes to warm through.
Remove from heat and swirl in the final 1 tablespoon of cold butter until the sauce turns glossy. Let rest 1 minute, then serve immediately over pasta, rice, or mashed potatoes with an extra grind of black pepper.