Preheat the oven to 350 degrees F (175 degrees C).

Melt butter in a large skillet over medium heat. Cook and stir onions in hot butter until soft and translucent, 7 to 12 minutes. Cool.

Stir cooled onions, Jarlsberg cheese, and mayonnaise together in a large bowl until well combined. Spread cheese mixture into 2 pie dishes. Sprinkle with paprika.

Bake in the preheated oven until the tops puff slightly and cheese is melted, 25 to 30 minutes.