Cook the mushroomsHeat olive oil in a skillet over medium heat. Add mushrooms and cook until softened and lightly golden, about 6–8 minutes. Stir in garlic, salt, and pepper; cook 30 seconds more. Remove from heat.
Prepare the pastryPreheat oven to 400°F (200°C). Place puff pastry on a parchment-lined baking sheet. Lightly score a 1-inch border around the edges, being careful not to cut all the way through.
Egg washBrush the scored border of the puff pastry with the beaten egg. This helps create a beautifully golden, glossy edge. Optional sprinkle with sesame or everything bagel seeds. Use a fork to gently prick the center of the pastry—this helps prevent it from puffing up too much while baking.
Assemble the tartSprinkle grated fontina evenly inside the border. Spoon the mushroom mixture over the cheese.
BakeBake for 18–22 minutes, until the pastry is puffed and deep golden and the cheese is melted and bubbly.
Finish & serveSprinkle with fresh parsley. Let cool slightly, then slice and serve warm or at room temperature