Heat grill to medium (350° to 450°) with an area left unheated for indirect heat. Toss potatoes in 1 tbsp. Garlic Roasted Chili Infused Olive Oil; grill flat side down until marks appear, 8 minutes. Turn over, moving to the indirect area. Cook until tender, 10 minutes. Let cool, then cut into chunks.
Whisk remaining 3 tbsp. oil, mustard, vinegar, oregano, capers, chili flakes, and anchovies in a large bowl. Gently mix in remaining ingredients.