Slice red onion. Heat 1 tablespoon olive oil in skillet. Sauté onions on medium heat, stirring occasionally, till medium brown. Cover and allow to steam on low heat. This will take about 10-15 minutes. 

Slice cherry tomatoes in half, and sprinkle lightly with salt. Allow to sit while preparing pastry.

Pre heat oven to 400 F.

Put a piece of parchment paper on sheet pan. Place puff pastry in center. Use sharp knife to score (do not cut all the way through) about one inch around outside

Use a fork, and generously poke holes all over the center section.

Bake for 10 minutes, turning pan half way through.

Pull pastry out of oven, and take the flat part of a fork and smash middle that has puffed up down.

Brush center of pastry with garlic oil. Spread shredded gruyer cheese in center. Sprinkle with herbs. 

Place onions over top of cheese. Sprinkle 1/2 of the freshly shredded parmesan over onions.

Top with cherry tomatoes, cut side up. Add a few grinds of fresh pepper, and top with remaining parmesan cheese.

Bake for a total of 30 minutes, turning half way through. If side crust is getting brown, and tomatoes have not quite cooked, cover lightly with foil.

When tart is done, allow to rest for at least 5 minutes.Use parchment to pick up tart, and move to a cutting, and serving board, and slide out the parchment. Use a sharp knife to cut into 4 squares.