Rinse the parsley and drain well. Pull the leaves from the stems and place them in a food processor with the Parmesan, garlic, salt, zest and juice from half the lemon (about 2 Tbsp juice). Pulse the ingredients until they are finely chopped. Slowly add the olive oil through the spout while the processor is running until a smooth paste forms. Set the pesto aside.
Heat a large skillet over medium flame. Add one tablespoon olive oil, then tilt the skillet to coat the surface. Add the tomatoes and cook 7-10 minutes, stirring occasionally. Avoid stirring the tomatoes too often to allow them time to blister on the hot skillet. As they cook the skins will burst and the tomatoes will release juice, which will thicken into a semi-sweet glaze. Season with salt and pepper to taste.
Bring a large pot of water to a boil for the pasta. Cook the pasta in the boiling water according to the package directions, or until al dente. Reserve a small amount of the starchy cooking water, then drain the pasta in a colander. Allow the pasta to cool slightly, then return it to the pot (with the heat turned off). Add the pesto, then toss to coat. If the pasta is too dry or clumps, sprinkle a little of the reserved cooking water on top to loosen.
Divide the pasta among five bowls, top with a scoop of the blistered cherry tomatoes, scraping up some of the sweet glaze from the skillet as well. Top each bowl with a fried egg, if desired.