For the Dressing and Fresh Aromatics:
3 tablespoons (45ml) fresh lime juice from 2 limes
2 tablespoons (30ml) fish sauce
2 teaspoons (15g) palm sugar, softened (see note)
1 small shallot (15g), thinly sliced (see note)
1 medium garlic clove (5g), thinly sliced
1 stalk lemongrass, bottom 4 to 5 inches only, outer leaves discarded, tender core thinly sliced into rounds (about 10g sliced lemongrass)
2 to 4 fresh Thai chiles (2 to 4g total), stemmed and thinly sliced into rounds (see note)
3 sprigs cilantro including stems (5g), cut into 1/2-inch pieces, plus extra leaves for garnish
1 scallion, green part only, sliced into 1/8-inch-thick rings (about 5g)
For the Fried Eggs:
2 large eggs
5 tablespoons (75ml) vegetable oil (see note)
Cooked jasmine rice
For the Dressing and Fresh Aromatics: In a small mixing bowl, stir together lime juice, fish sauce, and palm sugar until palm sugar is fully dissolved, about 15 seconds.
Add shallot, garlic, lemongrass, Thai chiles, cilantro sprigs, and scallion to dressing. Gently stir to combine and evenly coat solids with dressing. Set aside.
For the Fried Eggs: Line a plate or small tray with paper towels. Crack eggs into a small, shallow bowl. In a wok or 8-inch carbon steel or cast iron skillet, heat oil over high heat until it just begins to smoke. Holding the bowl closely above the oil, carefully slip the eggs into the oil in one swift and smooth motion to prevent oil from splattering; the egg whites should immediately puff and bubble around the edges. Cook undisturbed for 20 seconds, then begin swirling the pan to prevent eggs from sticking. Continue to cook, swirling pan constantly to promote even cooking of the whites, until the inner part of the whites close to the yolks are fully set, and the edges are wispy, golden brown, and crisp, about 1 minute. Using a large spoon or wok spatula, baste the yolks 2 to 4 times with hot oil until they just turn opaque and look like yolks on American-style, over-easy fried eggs. Using a slotted or wok spatula, carefully lift eggs out of oil, draining off as much excess oil as possible, and transfer to prepared paper towel–lined plate.
For Serving: Gently transfer fried eggs to a serving plate. Spoon the aromatics, herbs and dressing over the eggs, and garnish with cilantro leaves. Serve immediately with cooked jasmine rice on the side.