Heat the remaining 1 tablespoon oil in a large cast-iron skillet over medium-high heat until shimmering. Swirl the to coat the bottom with oil. Add the mushrooms and vigorously agitate pan, coating them in the hot fat. Arrange the mushrooms cut-side down and sear undisturbed for 2 minutes. Shake the pan and sear for 1 minute more. Transfer the cooked mushrooms to the bowl with the arugula and radishes.

Make the French toast: Meanwhile, whisk the eggs, buttermilk, half-and-half, cayenne, nutmeg, black pepper, and salt until incorporated in a shallow bowl or baking dish.

Dip 4 slices of the bread into the egg mixture. Turn to coat both sides, puncturing them a couple times as you do so with a fork.

Add 2 teaspoons of the oil to the pan and swirl to coat. Place over medium heat. Add the dipped bread and 1/2 tablespoon of the butter; drag the butter around the perimeter of the bread as it sizzles. Cook until golden-brown, flipping once and adding another 1/2 tablespoon of butter when you flip, 1 to 2 minutes per side. Transfer the French toast to plates. Repeat with the remaining bread.

Toss the salad mixture and spoon on top of the French toast. Season with flaky salt and black pepper, top with a dollop of creme fraiche if desired, and sprinkle with chives. Eat immediately.

RECIPE NOTES

Make ahead: The egg mixture can be made up to 3 days in advance and refrigerated.

Storage: Leftover French toast can be refrigerated up to 3 days.

(Melina Hammer is a writer for TheKitchn.com, a nationally known blog for people who love food and home cooking. Submit any comments or questions to editorial@thekitchn.com.)