Step 1

Place a rack in middle of oven; preheat to 350°. Whisk eggs and cream in a medium bowl until no streaks remain. Stir in Gruyère and arugula; set aside.

Step 2

Separate woody ends from asparagus spears; thinly slice ends and set aside.

Step 3

Heat 1 Tbsp. oil in a large cast-iron or ovenproof nonstick skillet over medium-high. Cook asparagus spears, tossing occasionally, until crisp-tender and blistered in spots, 5–8 minutes. Season with salt and transfer to a plate.

Step 4

Add 1 Tbsp. oil to same skillet. Cook red onion, garlic, oregano, and reserved asparagus ends, stirring occasionally, until onion is softened and asparagus is tender, about 5 minutes. Season generously with salt and pepper.

Step 5

Swirl remaining 1 Tbsp. oil in skillet and wait 30 seconds before pouring in reserved egg mixture. Arrange asparagus spears in a single layer on top. Cook, undisturbed, until egg mixture is set at the edges, about 3 minutes.

Step 6

Transfer skillet to oven and bake frittata until puffed slightly and center is just set, 15–17 minutes. Let cool in pan 15 minutes.

Step 7

Just before serving, scatter chives over frittata and season with more pepper.Do Ahead: Frittata can be made 3 days ahead. Let cool completely; wrap in foil and chill, or freeze up to 3 months. Reheat in a 300° oven until warmed through, 30–40 minutes.