Preheat the oven to 450 degrees F. On a large baking sheet, toss together the olive oil, potatoes, lemon zest, parmesan, and a small pinch each of salt and pepper. Lay the bacon flat, draped over the potatoes. Transfer to the oven and roast for 20 minutes, toss and continue roasting another 20-25 minutes, or until golden and the bacon crisp. If the bacon begins getting too crisp before the potatoes are done, remove the bacon from the oven. Meanwhile, make the garlic chili oil. Heat a medium skillet over medium heat. Add the olive oil, garlic, chili flakes, and a pinch of salt. Cook, stirring occasionally until the garlic is fragrant, 8-10 minutes. Stir in the basil, cook 30 seconds more. Remove from the heat and set aside. Remove the potatoes and bacon from the oven and transfer to a serving plate, draining off any excess grease. Arrange the eggs over the potatoes. Drizzle with garlic chili oil and finish with fresh dill and chives. Serve warm.