Preheat oven to 400 degrees F.
Place the feta and vegetables on a parchment-lined baking sheet. Toss vegetables and drizzle cheese with 1 tablespoon of olive oil and 1 teaspoon of salt.
Bake in the oven for 15 minutes or until the tomatoes have burst.
Meanwhile, boil the pasta in very salty water according to package directions. Drain and set aside, reserving ½ cup of pasta water.
When the vegetables and feta are done baking, combine the feta, reserved pasta water, and pasta in a large bowl. Stir the feta is evenly dispersed over the pasta. Then add the vegetables, remaining olive oil, remaining salt, pepper, lemon juice, and arugula and stir gently till combined.
Serve immediately or save in the refrigerator for up to 4 days.