First things first, make sure you are starting with a thawed out puff pastry sheet. Set your oven to 400 °F. On a lightly-floured surface, roll the puff pastry dough into a 16-by-10-inch rectangle. If you aren't a fan of the rustic look, you can trim the extra and cut straight lines. Up to you!
Next, we need to prepare the pastry dough for baking and create the "crust" area. Move your rolled out pastry dough tp a sheet pan lined with parchment paper. Using a knife, lightly score the pastry dough 1 inch in from the edges, forming a rectangle. Don't pierce all the way thru the dough. This is more like an indented mark. Next, grab a fork and pierce the dough inside the rectangle at 1/2-inch intervals. Bake for 10-15 minutes, rotating halfway thru. Pastry should come out golden.
While the pastry is baking, it's time to make the pesto-whipped goat cheese! I like to do this part with my food processor, but if you don't have one, you can mix this in a bowl. Just make sure that the goat cheese is definitely softened.
Add the softened goat cheese to the bowl of your food processor and blend until it achieves a creamy, soft texture. About 35 seconds or so! Next, add the rest of the ingredients for the pesto-whipped goat cheese: 3 tbsp pesto, 2 garlic cloves (grated), zest of 1 lemon, juice of 1/2 lemon, 1 tsp honey, 2 tbsp Italian seasoning blend, 1/2 tsp pepper, 1/2 tsp kosher salt, and 1/2 cup basil leaves. Process until everything is combined. Taste and adjust salt + pepper to your liking.
Time to assemble! Gently spread the goat cheese mix on top of the tart pastry - make sure not to rip the pastry by going too rough. Remember, it doesn't have to be perfect! Once the pesto-whipped goat cheese is spread out, place the sliced tomatoes on top.
Whisk the egg in a small bowl, and brush the edges of the tart (the "crust") with the egg wash. Bake for 20-25 minutes, making sure to rotate the tart halfway thru. Allow the tart to cool for 10 minutes before cutting. Top with fresh basil and flaky sea salt. Serve Immediately.