Pre-heat the oven to 255° F.
In an oven-safe dish, dress the tomatoes with 2 teaspoons of olive oil, the balsamic vinegar, and the agave nectar. Season with salt and pepper to taste and set aside.
Chop the mushrooms into 1/4-inch cubes and place in a bowl. Add the onions, garlic, 1 tablespoon of parsley, 4 teaspoons of olive oil, the soy sauce, and the Worcestershire sauce. Stir to coat all the cubes evenly, then salt and pepper to taste.
Pour the prepared mushroom cubes into another oven safe dish, spreading in a single layer so that the chopped mushrooms roast evenly.
Transfer both dishes to the pre-heated oven.
Slowly roast the mushrooms until they are wilted and very aromatic, about one hour.
Remove the mushrooms from the oven and allow to cool. Transfer to a closed container and store in the refrigerator until ready to assemble the tart.
After removing the mushrooms, shake the oven dish containing the tomatoes so that the tomatoes roll over in the pan. Continue baking until the tomatoes are wilted, the skins are broken, and everything is somewhat caramelized from the balsamic and agave (about 3 more hours). Shake the dish every hour or so to roll the roasting tomatoes.
Remove the tomatoes from the oven, allow them to cool completely, then add them to the same container with the roasted mushrooms. You can assemble the tart at this time or keep the container in the refrigerator for a day or two before preparing the tart.
To assemble the tart, pre-heat the oven to 425° F.
Use a rolling pin to slightly stretch the puff pastry sheet on a lightly floured surface, until the rectangle is about 1/4-inch larger on all sides. This helps prevent the pastry from puffing up too high while baking.
Transfer the puff pastry to a parchment-covered sheet pan with a lip.
Next, spread the cream cheese over the puff pastry. Sprinkle lightly with salt to season.
Remove the mushrooms and tomatoes from the refrigerator. Stir to combine the ingredients and break up the tomatoes a bit. The mixture should look somewhat like a paste made up of coarse pieces.
Spread the tomato and mushroom mixture evenly over the cream cheese. Sprinkle a teaspoon of finely chopped onions over the tomatoes and mushrooms.
Fold the edges of the puff pastry by about 1 inch over the topping.
Lightly spray the folded edges with olive oil cooking spray to enhance browning, if desired.
Bake for 20 minutes, or until the folded edges of pastry are a light golden brown.
Remove from the oven, lightly drizzle with olive oil, spanning both topping and crust. Garnish with fresh parsley, cut to desired portion size, and serve warm.