Preheat the oven to 375 degrees F.
Carefully fill the cavity of the peppadew peppers with the herbed goat cheese.
Place the stuffed peppers into a small, oven safe dish.
In a small bowl, whisk together the olive oil, white wine vinegar, and pesto until well combined. Drizzle ¾ of the mixture (reserving the last bit for later) over the stuffed peppers. Sprinkle the top with the chopped walnuts.
Transfer to the oven and bake until hot, about 10 minutes.
Remove from the oven and gently give the peppers a toss. Drizzle the top with the remaining pesto mixture. Serve immediately with toothpicks and enjoy!