Preheat oven to 375 degrees. Toss potatoes with shallots, 1/4 cup oil, the thyme, and 1/2 teaspoon salt in a large bowl; season with pepper. Arrange in a single layer on a rimmed baking sheet. Roast, flipping once, until edges are golden brown, about 20 minutes per side.
Melt butter with remaining 2 tablespoons oil in a large skillet over medium heat. Add bacon slices in a single layer, and cook, flipping once, until just browned, about 3 minutes per side.
Divide potato mixture among plates, and season with salt. Arrange bacon on plates with the potatoes, dividing evenly. Serve with eggs. Season with pepper.