Preheat the oven to 400°F. Grease the bottom and the sides of a 13 x 9 inch pan or a rectangular 12-inch long gratin dish liberally with the butter and spread the minced garlic evenly on the bottom.
Assemble the gratin: Combine the potato slices with the cream, 1 cup walnuts, 1/2 cup Parmesan cheese, Gruyere cheese, milk, nutmeg and a generous handful of salt. Mix to blend. Taste the cream for seasoning. Transfer to the prepared baking dish and spread to form an even layer.
Make the crust and cook the gratin: Combine the panko with the remaining 1/2 cup walnuts and remaining 1/2 cup Parmesan cheese. Top the potatoes with the crust. Cover the dish with aluminum foil and place in the center of the oven. Bake for 20 minutes then remove foil and continue baking for an additional 25-30 minutes or until potatoes in center are fully tender when pierced with the tip of a knife. Remove from oven and let sit for 15-20 minutes.
Roast the tomatoes: Arrange the tomato halves, cut side up, on a baking sheet. Season with salt and drizzle with 1 tbsp. of olive oil. Place the tray in the center of the oven and bake until the tomatoes are roasted and tender, 12-15 minutes. Set aside.
Make the vinaigrette: Meanwhile, whisk together the remaining 3 tbsp. olive oil, red wine vinegar and mustard. Set aside.
Finish the gratin: Serve the gratin in the dish it was cooked in. Top with the tomatoes and drizzle the top with the vinaigrette.