Preheat oven to 400 degrees.
Spray a 15 x 10-inch nonstick baking sheet with cooking spray. Set aside.
Heat olive oil in a nonstick skillet or saute pan over medium-high heat. Add the asparagus, reduce heat to medium and cook 1-2 minutes or until it turns bright green. Add the scallion and cook 1 minute. Set aside to cool.
Lightly flour a work surface. Unfold the puff pastry sheets onto the floured work surface and gently press and repair the folds. Stack the sheets so they overlap by 1-2 inches to form one large puff pastry sheet.
Roll the newly formed single sheet out to form a rectangle that is approximately 1-inch larger than the sheet pan, using it as a guide.
Carefully transfer the pastry to the prepared sheet pan. Fold the edges down into the sheet pan to form an even crust around the rim. Dock the crust with a fork in numerous places to let steam escape.
Sprinkle half the Asiago or Parmesan cheese over the crust. Top with the artichokes, scallion, and the asparagus last, distributing them evenly. Sprinkle the remaining Asiago or Parmesan over the vegetables.
Whisk the eggs, ricotta cheese, and half-and-half together until smooth. Add the salt and a pinch or two of black pepper.
Pour the egg mixture over the vegetables and gently smooth.
Top the tart evenly with goat cheese.
Place the tart in the oven and bake for 10 minutes. Lower the oven temperature to 375 degrees and bake for another 25 minutes or until the crust is lightly browned.
Cut into pieces and serve.