Heat 1 tablespoon oil in a large (at least 12-inch) skillet over medium-high heat. Add the chicken, season with salt and pepper, and cook until the cubes are golden brown on the outside but not quite cooked through, about 4 minutes. Remove the chicken with a slotted spoon to a plate.
Add the remaining tablespoon of oil to the pan and heat over medium heat. Add the garlic and saute for 1 minute, until just golden brown. Add the tomatoes, season with salt and pepper, and stir for about 2 minutes, until they start to soften. Add the broth and cream, turn the heat to medium-high, and bring to a simmer. Add the chicken and simmer for 2 minutes until cooked through.
Meanwhile, cook tortellini according to package directions, taking them out 1 minute ahead of fully tender. Stir the almost-cooked tortellini, spinach, and ½ cup Parmesan into the sauce, and stir until the spinach is wilted and incorporated into the sauce, about 1 minute.
Serve hot, with additional Parmesan passed on the side.
Notes
If you wanted to use 1 cup broth and ½ cup cream (inverting the proposed proportions), you could do that for a slightly lighter sauce.
If you want to make a vegetarian version of this, use vegetable broth, make sure the tortellini has no meat, and skip the cubed chicken. You can also think about adding in some cooked cubed tofu.