Heat olive oil and butter in a skillet over medium heat.
Add diced pear and cook for 2–3 minutes, until just softened.
Remove from heat.
In a medium bowl, combine chopped arugula, walnuts, and blue cheese. Add in the cooked pear. Season with a little salt and pepper. Stir together. Set aside.
Lay pork chops flat on a cutting board. Using a sharp paring knife, cut a deep horizontal pocket into the side (about ¾ of the way through, without cutting all the way through).
Season both sides — and inside the pocket — generously with salt and pepper.
Spoon the pear mixture evenly into each pocket. Press gently to pack the filling and gently close.
Preheat oven to 375°F (190°C).
Heat a drizzle of olive oil and 1 tbsp of butter in an oven-safe skillet over medium-high heat. Add fresh thyme sprigs.
Sear pork chops for 2–3 minutes per side, until golden brown.
Transfer skillet to oven and bake for 12–15 minutes, or until the pork (not the filling) reaches 145°F (63°C)internally.
Rest for 3–5 minutes before serving.
Drizzle with balsamic glaze (if desired) and serve over mashed potatoes, or with your favorite grains or veggies.