Heat a skillet over medium heat. Add chopped shallot and cook until soft, about 2-3 minutes. Add garlic and mushrooms, cooking until browned. Season with 1/2 tsp salt, 1/4 tsp pepper, and thyme. Remove from heat and cool. In a bowl, combine the mushroom mixture with shredded Gouda, panko breadcrumbs, and parsley.

Preheat oven to 400°F (200°C). Butterfly each chicken breast by slicing horizontally through the thickest part, without cutting all the way through. Open each breast like a book and season inside and out with remaining salt and pepper.

Divide the filling evenly among the chicken breasts, spooning it into the pocket of each one. Fold the top over to close and secure with toothpicks if necessary.

Heat olive oil in a large, oven-safe skillet over medium-high heat. Place the stuffed chicken in the skillet and sear for 3-4 minutes on each side until golden brown.

Transfer the skillet to the preheated oven. Bake for 15-20 minutes, or until the chicken is cooked through and a meat thermometer inserted into the thickest part reads 165°F (74°C).

Remove the chicken from the oven and let it rest for 5-10 minutes before slicing and serving. Remember to remove the toothpicks.