If you are using an oven to cook your peaches, preheat it to 400 degrees F (220 degrees C). If using a grill, preheat it to the same temperature.
Combine Dijon Mustard (1 tablespoon), White Wine Vinegar (2 tablespoon), Olive Oil (2 tablespoon), and Honey (1 tablespoon) in a bowl and whisk to combine. Taste and season with Salt and Pepper (to taste) and set aside.
Remove the pit from your Peach (2) and cut into thin slices.
If cooking in the oven, arrange peaches and Walnut (1/3 cup) on a baking sheet and roast for 15 minutes, with an additional 5 minutes if needed. If preparing on the grill, brush with olive oil and place cut-side down on the grill and cook for 4-5 minutes on medium heat, flip and remove after another 4-5 minutes.
Prepare your salad by setting Arugula (200 gram) on a bowl or plate, placing peaches on top then drizzling with the dressing. Garnish with crumbled walnuts.