Preheat the oven to 400°F (200°C).
Pat chicken dry and rub with olive oil. In a small bowl, mix smoked paprika, garlic powder, dried thyme, salt, and pepper. Rub the seasoning all over the chicken.
Heat a large oven-safe skillet over medium-high heat. Sear the chicken for 3-4 minutes per side, until nicely browned. Transfer to a plate.
Reduce the heat to medium. Add butter to the skillet. Once melted, add mushrooms and cook, stirring occasionally, until the moisture has evaporated and they're browned, about 8-10 minutes.
Stir in shallot and cook for a couple of minutes, until softened. Add garlic and cook for 30 seconds more.
Add sun-dried tomatoes and orzo. Cook for 1 minute, stirring frequently, until the orzo is lightly toasted. Pour in white wine and simmer until almost completely reduced. Add chicken broth and bring to a gentle simmer. Cook for 5 minutes, stirring occasionally.
Reduce the heat to low. Stir in heavy cream and Parmesan until smooth and combined. Give the sauce a taste and season with salt, if needed. Fold in spinach until wilted. Nestle the chicken on top of the orzo.
Transfer the skillet to the oven and bake for 12-16 minutes, or until the chicken reaches 165°F (74°C) and the orzo is tender. Garnish with fresh thyme and serve.