Preheat oven to 400 degrees F. Line a baking sheet with a Sil-Pat or parchment paper.
In a medium mixing bowl, stir together the ricotta and jack cheese until well combined.
Place awonton wrapper on your work surface (cutting board, plate, something flat). Spoon 1/2 tablespoon cheese mixture into the middle of the wonton wrapper. Place a 1/4 teaspoon sun dried tomato pesto on top of the cheese.
Dip your finger into the water and run it along one edge of the wonton wrapper. Repeat with the other 3 sides. Bring two opposite corners of the wonton together in the middle above the cheese and gently pinch them together. Bring up one of the remaining corners to the middle and pinch together with the frist two. Use your fingertips to pinch the edges that form together to seal them. Bring up the last corner, pinching it in the middle with the other corners, and then sealing the edges.
Place the wonton on the prepared baking sheet. Repeat with the rest of the wontons, cheese mixture, and pesto until you've used all the ingredients. Space the wontons about 1-inch apart.
Bake for 10 minutes, or until the cheese is melty and the "X" edges on the wontons have begun to brown.
Remove from the oven and let cool on the baking sheet for 5 minutes. Transfer to a platter and serve immediately.
Notes
If you'd prefer, you can mix the sun dried tomato pesto into the cheese mixture. It won't hurt anything. I just like the layered effect inside. And if sun dried tomatoes aren't your jam, you can substitute regular pesto and these will still be delightful!