Bring a large pot of water to a boil. Cook pasta 1 minute less than package directions.
Carefully drain pasta, season with ½-tabelsppon olive oil to prevent from sticking, cool down flat on a sheet pan. Store in the fridge in an airtight container.
Meanwhile, prepare pesto. In a food processor pulse garlic, salt, pepper, pumpkin seeds until thinly ground. Stir in greens, remaining olive oil, lemon juice and zests and a few ice cubes; process to incorporate; fold in cheese.
Place pasta in a bowl, pour pesto on it, add chicken and tomatoes; mix well.
Ideally let sit 20 minutes at room temperature before serving.
