Preheat oven to 400ºF and line 2 to 3 baking sheets with parchment paper.

Heat olive oil in a small skillet over medium heat. Add onion, garlic, and chili flakes. Cook until softened and translucent, about 3 to 4 minutes. Remove from pan and let cool.

In a mixing bowl, add spinach and artichokes, then stir in Gruyère and Parmesan. Season with salt and pepper to taste.

Unfold one puff pastry sheet on a lightly floured surface. Lightly flour both sides if wet or sticky. Top with half the vegetable-cheese mixture, leaving a ½-inch border.

In a small bowl, beat egg with 1 tablespoon water. Brush the furthest edge with egg wash. Roll up pastry, jelly-roll-style, sealing the roll with the egg wash edge.

Repeat with the other puff pastry sheet and remaining filling.

Cut each roll into ½-to-¾-inch-thick slices. Lay slices flat 2 inches apart on the baking sheets. Lightly brush with egg wash.

Bake for 25 to 30 minutes, or until golden, rotating sheets halfway through.

Serve warm or at room temperature.