Combine chicken, garlic, tamari, vinegar, bay leaves, and peppercorns in a bowl. Marinate at room temperature 30 minutes, or refrigerate up to overnight for deeper flavor.
Heat oil in a large skillet or Dutch oven over medium-high heat. Lift chicken from the marinade (reserve the marinade) and sear 3-4 minutes per side until golden brown.
Pour the reserved marinade and brown sugar over the chicken. Bring to a boil, then reduce heat to low, cover, and simmer 25 minutes until the chicken is tender.
Uncover and simmer 8-10 more minutes, spooning sauce over the chicken occasionally, until it thickens into a glossy coating.
While the chicken cooks, toss the cucumber slices with salt, rice vinegar, and sugar. Let sit at least 15 minutes, tossing once or twice.
Divide steamed rice among 4 bowls. Top with adobo chicken and plenty of sauce, then finish with the quick-pickled cucumber.
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