Cook the tortellini according to package directions. Drain and pour them into a large mixing bowl. Set the tortellini aside to cool.
Place the sliced eggplant, zucchini, red pepper, and asparagus in a colander and sprinkle the vegetables with salt, pepper, and oregano. Toss to coat with the seasoning and let the vegetables sit for 15 minutes.
While the vegetables rest, heat the grill to medium-high heat and oil it or spray it with cooking spray.
Drizzle the seasoned vegetables with olive oil and lay them on the grill. Grill the vegetables for about 4 minutes or until they are tender and have grill marks on the side near the flame. Flip the vegetables and grill for another 3 minutes or until the second side is lightly charred.
When the vegetables are charred and tender, remove them from the grill and let them cool.
Slice the grilled vegetables into bite-sized pieces (about 1 ½ inches) and add them to the bowl with the tortellini.
Add the artichoke hearts, olives, radicchio, salami, and cheese, to the bowl.
Combine the pesto and red wine vinegar in a small mixing bowl or jar. Mix well to combine and pour the dressing over the salad. Toss lightly to combine the ingredients.
Serve immediately or refrigerate until ready to serve.