In a very large skillet, heat the olive oil over medium-high heat. Sear the chicken for about 3 minutes on each side or until browned and just barely pink in the center. Do this in batches if needed, and remove the chicken to a plate and set aside.
Return the skillet to medium heat, add the shallots, and sauté for 2 minutes until they start to become tender. Add the chicken broth and bring to a simmer, scraping up any browned bits from the bottom. Stir in the heavy cream, oregano, and thyme, and heat until the edges of the sauce start to bubble. Sprinkle in the Fontina and the Parmesan cheeses and stir until they are melted. Stir in the spinach and the sundried tomatoes and keep at a very low simmer until the spinach is wilted, about 2 minutes.
Return the chicken to the pan and allow it to heat through, about 2 minutes. Serve the chicken with the sauce over hot rice or pasta.
Notes
Try to find real sun-dried tomatoes, which won’t be hard little dried-up disks, but rather pliant, brick red, little chewy bites then that will make all the difference. If there is a store that sells good Italian ingredients in your world, seek them out there. If you want to use oil-packed sundried tomatoes, you can, but use paper towels to blot excess oil before chopping them.