Heat the oven to 375°F with the rack in the middle. Pat both tenderloins dry with paper towels. Fold each thin tail under and tie it with twine so the pieces cook evenly.

Mash the softened butter with all the chopped herbs using a fork. Stir in both zests and the garlic. Stop zesting at the colored layer. The butter should look flecked with green and spread like thick frosting.

Rub the salt and pepper over every side of both tenderloins. Let them sit while the skillet heats, about 5 minutes.

Heat the oil in the 12-inch skillet over medium-high until it shimmers, about 2 minutes. Lay both tenderloins in, with a finger of space between them. Sear 3 minutes without moving them, then flip and sear 2 minutes more.

Take the skillet off the heat and wait 2 minutes. Spread two-thirds of the herb butter over the tops and sides with the back of a spoon. Save the rest for the sauce.

Slide the skillet into the oven. At 18 minutes, slip the probe into the thickest part, away from the tail. Pull the turkey at 160°F, usually around 23 minutes.

Move the tenderloins to a board and tent loosely with foil for 10 minutes. The temperature climbs to 165°F as they rest.

Wrap the skillet handle in a towel. Set the pan over medium heat and whisk in the flour for 60 seconds. Pour in the broth and scrape up the browned bits.

Simmer for 4 to 5 minutes until it coats a spoon. Whisk in the leftover herb butter.

Snip off the twine. Slice against the grain into ½-inch rounds. Fan them on a platter and spoon on the sauce. Tuck in the orange slices and sage leaves.