Prepare tortellini according to package directions. Drain and place in a bowl.
Combine avocado, peas, basil, parsley, garlic, nuts, lemon zest and juice, ¼ tsp. salt and pepper in a blender or food processor. While pulsing, drizzle in up to ½ cup olive oil, scraping sides regularly with a spatula, until pesto reaches desired consistency.
Taste and adjust seasoning, if necessary. Set aside. Heat a cast iron grill pan to medium-high. Drizzle tomatoes with olive oil and season with a dash of salt and black pepper.
Place tomatoes in the hot pan and cook 1-3 minutes, until tomatoes are blistered. Mix about half the pesto with the tortellini until coated.
Serve hot or cold with blistered tomatoes and garnish with Parmesan cheese.