Fill a saucepan with lightly salted water then bring to a rolling boil over high heat. Once the water is boiling, stir in the linguine then return to a boil. Cook the pasta uncovered, stirring occasionally until the pasta has cooked through but is still firm to the bite, about 11 minutes. Drain well in a colander set in the sink.
While the pasta is boiling, sprinkle the chicken with salt and black pepper. Heat the olive oil in a frying pan over medium heat then cook the chicken pieces until lightly browned, about 10 minutes, stirring frequently. Stir in the garlic cloves, mushrooms, roasted red capsicum and artichoke hearts; reduce heat to a simmer then cook until the mushrooms begin to give off their juices, 5 to 8 minutes. Stir in the spinach then simmer just until the leaves are wilted, about 2 minutes.
Transfer the cooked linguine into a bowl then toss with the basil pesto. Divide the pasta between 2 plates and serve topped with the chicken mixture. Sprinkle Parmesan cheese over each plate to serve.