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Step 1
In a large pot over medium-high, combine the broth, smashed garlic cloves, sliced ginger and peppercorns. Bring to a simmer, then fully submerge the chicken breasts, meat side down. Cover, reduce to low and cook, adjusting the heat as needed to maintain a bare simmer, until the thickest part of the breast reaches 160°F, 20 to 25 minutes.
Step 2
Transfer the chicken, meat side down, to a medium bowl. Pour 1 cup of the hot cooking liquid over the chicken and set aside until cool enough to handle, about 30 minutes.
Step 3
Meanwhile, strain the cooking liquid through a fine mesh strainer set over a large bowl; discard the solids. Reserve 2½ cups of the liquid; the remainder can be saved for another use. Reserve the pot.
Step 4
When the chicken breasts are cool enough to handle, remove the meat from the bones, keeping each breast in a single piece. Discard the bones. Return the meat to the bowl.
Step 5
Set the pot over medium and add the chicken skin. Cook, stirring and scraping often to prevent sticking, until the skin is rendered and crisp, 3 to 5 minutes. Add the shallots, the grated garlic and grated ginger and cook, stirring, until they begin to brown, 1 to 2 minutes. Add the rice and cook, stirring, until the grains are coated with fat, 2 to 5 minutes. Carefully stir in 2 cups of the reserved cooking liquid (reserve ½ cup of the remaining liquid for the dipping sauce), scraping the bottom of the pot. Cover and bring to a boil, then reduce to low and cook until the rice absorbs the liquid, about 12 minutes.
Step 6
Remove the pot from the heat and let stand, covered, for 10 to 15 minutes. Fluff the grains with a fork and discard the chicken skin. Transfer the rice to a serving bowl and sprinkle with scallions. Cut the chicken breasts crosswise into ½-inch slices and arrange on a platter with the cucumbers or lettuce. Serve with the rice, dipping sauce and/or kecap manis.