Peel the potato and cut into thin slices (about ¼ inch). Drop into a saucepan of well-salted boiling water and cook over medium-high heat for 6-7 minutes, until the potato is cooked but not mushy. Drain and set aside.

While the potato is cooking, cut the garlic, chiles, and half of the onion into thick slivers. In a small skillet, heat 1 tablespoon of the oil to rippling over medium-high heat. Add the slivered vegetables and cook, stirring constantly, until the onion is translucent but still has some crunch, about 2-3 minutes. Set aside.

Cut the remaining half of the onion into thin half moons. In a nonstick or well-seasoned 9-inch omelet pan or skillet, heat the remaining 2 tablespoons of the oil over medium heat until fragrant. Add the sliced onion and cook until translucent, about 3 minutes.

In a mixing bowl, lightly beat the eggs with 1 teaspoon salt. Pour the mixture into the pan; reduce the heat to low and add the reserved sliced potato. Cook, running a spatula around the edges to let the uncooked egg trickle to the bottom of the pan, for about 4 minutes or until almost set. Loosen by running the spatula around the edges and slide out onto a plate. Invert back into the pan and cook until golden and lightly set, about another 2 minutes.

Fold over the omelet into thirds and slide out into a shallow serving bowl or deep plate. Scatter the garlic-chile-onion garnish over it and pour the hot broth over the top. Serve at once.