Meanwhile, heat a large skillet over medium heat. Add chopped bacon; cook, stirring occasionally, until rendered and crispy, about 8 minutes. Using a slotted spoon, transfer bacon to a paper towel-lined plate to drain, reserving about 3 tablespoons drippings in skillet.

While bacon cooks, sprinkle chicken evenly with pepper and 1/4 teaspoon of the salt. Add chicken to skillet with drippings; cook over medium-high, until chicken is browned and cooked through (a thermometer inserted into thickest portion of chicken registers 165 degrees F (73 degrees C)), 5 to 6 minutes per side, reducing heat if bottom of pan gets too dark. Transfer chicken to a plate; set aside until cool enough to handle, about 10 minutes. Chop chicken into bite-size pieces.

Reduce heat to medium, and add sundried tomatoes and shallot. Cook, stirring often, until softened, about 2 minutes. Add garlic, Italian seasoning, crushed red pepper, and remaining 1 teaspoon salt. Cook, stirring constantly, until fragrant, about 30 seconds. Add tomato paste; cook, stirring constantly, until deepened in color, about 1 minute.

Pour in chicken broth; cook, stirring and scraping constantly to deglaze the skillet, about 1 minute. Stir in cream and bring to a simmer over medium. Simmer, stirring occasionally, until slightly thickened, 3 to 5 minutes.

Add tortellini to boiling water, and boil until tortellini are tender and float to the surface, 3 to 5 minutes. Reserve 1 cup cooking water. Drain.

Stir Parmesan cheese, reserved cooked bacon, reserved chopped chicken, and tortellini into skillet with cream mixture. Cook, stirring and tossing constantly, until evenly coated in sauce. Add reserved cooking water, 1/4 cup at a time, if necessary to maintain a creamy consistency. Divide mixture among 6 bowls; garnish with additional Parmesan cheese and a generous scattering of fresh basil.