Bring a large pot of salted water to a boil.
Add the chicken tortellini and cook until tender, 5–8 minutes; drain and set aside.
Heat the olive oil in a large skillet over medium heat, add the sliced mushrooms, and sauté until soft, about 4–6 minutes; remove mushrooms from the pan and set aside.
In the same skillet over medium heat, add the half and half, crumbled feta, grated Parmesan, Italian seasoning, and fresh cracked pepper; whisk continuously until the cheeses melt and the sauce thickens, about 7–10 minutes.
Remove the skillet from the heat, return the cooked tortellini and sautéed mushrooms to the sauce, then add the baby spinach in handfuls and toss until wilted and evenly coated.
Adjust seasoning with additional pepper if desired and serve immediately.