Step 1

Heat 2 Tbsp. oil in a large nonstick skillet over medium. Add potatoes, season with salt, and cook, tossing occasionally, until well browned around the edges and just slightly undercooked, 10–12 minutes. Transfer potatoes to springform pan and let cool; reserve skillet.

Step 2

Lightly coat sides of pan with oil. Flatten potatoes slightly with the back of a spoon, packing into the seam where 2 parts of springform pan meet.

Step 3

Preheat oven to 300°. Heat remaining 3 Tbsp. oil in reserved skillet over medium. Cook onion, tossing occasionally, until softened but not browned, 8–10 minutes. Add kale a handful at a time and cook, stirring, until just softened but not limp, 5–6 minutes. Season with salt. Let cool slightly.

Step 4

Whisk eggs, cheese, and yogurt in a large bowl; season with salt and pepper. Set springform pan on a parchment- or foil-lined rimmed baking sheet. Top potatoes with half of kale and onions, then pour in egg mixture. Gently press remaining kale and onions into surface of egg mixture.

Step 5

Bake quiche until edges have puffed up slightly and top is just set with no liquid egg remaining, 55–75 minutes. Let cool before slicing.