Lightly coat the insert of a 6-quart slow cooker with nonstick cooking spray. Add the rinsed rice, mushrooms, and shallots and spread them into an even layer.
Whisk together the chicken stock, white wine, melted butter, garlic, Dijon mustard, 1 teaspoon kosher salt, and ¼ teaspoon black pepper. Pour evenly over the rice and vegetables.
Pat the chicken thighs dry and season with the remaining ½ teaspoon kosher salt and ¼ teaspoon black pepper.
Optional: For deeper flavor and better color, heat the olive oil in a large skillet over medium-high heat. Brown the chicken for about 2 minutes per side. The chicken does not need to cook through. Transfer it directly to the slow cooker. For the easiest one-pot version, skip this step.
Arrange the chicken thighs in a single layer over the rice, pressing them lightly into the liquid without completely burying them.
Cover and cook on HIGH for 2 to 2½ hours. Avoid lifting the lid during the first 2 hours. Beginning at 2 hours, check for doneness. The chicken should reach at least 165°F in its thickest portion, and the rice should be tender with most of the liquid absorbed.
Remove the chicken to a plate. Add the spinach, Parmesan, butter, lemon zest, and 2 teaspoons lemon juice to the rice. Gently fluff and fold everything together until the butter and Parmesan melt and the spinach begins to wilt.
Return the chicken to the slow cooker. Cover and let everything rest for 5 minutes. The rice will continue absorbing moisture during this time, so do not add additional stock before the rest unless the rice is clearly undercooked.
Taste the rice and adjust with salt and pepper as needed. Add another small squeeze of lemon only if the dish needs additional brightness. Serve the chicken over generous spoonfuls of the creamy mushroom-Parmesan rice.