Preheat oven to 450 degrees F.
Bring a pot of salted water to a boil for the tortellini. Place the peppers in a roasting pan and roast in preheated oven, checking every 15 minutes, and turning them with tongs until the skin is fully wrinkled and charred black. White the peppers are roasting, boil tortellini until al dente, drain, and set aside to cool. Put the charred peppers into a bowl filled with a couple of inches of ice water. Once cooled, you can then use your fingers to work quickly to slip off and discard the skins of the peppers while they are in the water. Transfer them to a plate, peel away any remnants of the charred skins, slice open and remove the stem and seeds, then julienne the peppers and set aside.
Through the feed opening of a running blender, add scallions, garlic cloves, sun-dried tomatoes, and 1/2 cup of the fresh basil leaves (packed), reserving the rest of the basil. Add the vinegar and blend until a paste is formed, then leaving the blender running, add the olive oil in a slow steady stream allowing the mixture to emulsify. Season the dressing with salt and pepper, to taste.
Julienne the rest of the basil (except for the sprigs for garnish). Toss with the tortellini, julienned red bell peppers, and dressing. Transfer to serving dish and decorate with reserved basil sprigs. Can be served at room temperature or chilled.
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