Heat olive oil in a large skillet over medium heat.
Season chicken slices with salt and add them along with a quarter cup of chopped sun-dried tomatoes to the skillet; cook, turning occasionally, for about 5 to 10 minutes until fully cooked.
Remove the chicken and sun-dried tomatoes from the pan, keeping the oil in the skillet.
Add the trimmed asparagus and season well with salt; stir in the remaining sun-dried tomatoes and sauté for 5 to 10 minutes until the asparagus is tender, then transfer to a plate.
Prepare the tortellini according to the package directions and drain.
Return the cooked chicken to the skillet and stir in the basil pesto; warm through on low to medium heat for 1 to 2 minutes.
Mix in the cooked tortellini and halved cherry tomatoes, combining everything evenly; add extra pesto if desired.
Taste and add more salt if needed.
Serve the chicken, tortellini, and tomatoes alongside the sautéed asparagus.