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.