Preheat oven to 425°F. Line two baking sheets with parchment paper and set aside.
Unfold the puff pastry sheets and roll out slightly to remove the creases. Cut each sheet into six even rectangles so you end up with twelve pieces. Place six onto each baking sheet. Use a sharp pairing knife to score a rectangle on each puff pastry piece's edge. Don't cut all the way through. Then use a fork to prick holes all through the center of each.
Brush the puff pastry tarts with egg wash and bake until deep golden brown and flaky, 20 to 25 minutes. Remove from the oven and allow to cool. Once cool, press down on the tarts to remove flatten them a bit, especially if they've puffed up a lot. Set aside.
Bring a medium saucepan to a boil. Season with a liberal pinch of salt. Then add in the lima beans. Blanch for about 1 minute, then use a slotted spoon to remove to a large bowl. Bring the same water to a boil once again and then add the peas. Blanch for a minute as well and then use a slotted spoon to remove the peas. Add half of them to the same bowl as the lima beans and the other half to a food processor. Allow to cool.
Once cooled, add the pepitas, parmesan, mint, basil, garlic, lemon juice, 1 teaspoon salt, and 1/2 teaspoon black pepper to the food processor with the peas. Plus a few times until finely chopped. While the machine is running, slowly stream in the olive oil and process until a thick pesto forms. Give it a taste and adjust seasoning accordingly, adding more salt or pepper as needed.
Season the lima beans and peas with a tablespoon of olive oil and a pinch of salt and pepper. Give it a toss to evenly combine.
To assemble the tarts, spread each cooled puff pastry with ricotta. Top with pea pesto and garnish each with parmesan, fresh mint and basil. Season lightly with salt and lots of fresh ground black pepper. Serve immediately and enjoy!