Combine water, 1 cup of sugar and 1 cup of salt in a large container. Stir until dissolved. Add chicken, cover and refrigerate for at least 1 hour and no more than 6. Remove chicken and discard brine.
Preheat oven to 180°. Pack chicken snugly into a pot or other ovenproof vessel. Tuck bacon strips around the chicken. Pour grapeseed oil over the chicken to cover. Bake for 50 minutes.
Remove from oven and cool. Chill chicken in the fat. This step can be done up to a week in advance. When you are ready to serve the dish, remove the chicken from the fat and drain on a plate.
Make a quick cucumber pickle: slice the cucumbers into thin slices. Toss with remaining sugar and salt and allow to sit until ready to serve.
To make the ginger scallion sauce, combine all ingredients and let sit for 10–15 minutes for flavors to develop.
Heat a cast-iron grill pan or heavy skillet over medium-high heat for 1–2 minutes, until the pan is hot. Add chicken skin-side down and brown deeply, 3–4 minutes, using a small, heavy skillet to weigh it down. Transfer chicken to a cutting board.
Portion the rice among 4 deep soup bowls. Use the back of a soup spoon to create a shallow indention in the middle of each bowl of rice and slide a poached egg into it. Divide cucumber among the bowls, nestling them together in a mound. Cut the chicken into ½-inch thick slices, and fan around the egg. Sprinkle with scallions and drizzle with ginger-scallion sauce. Garnish with cilantro leaves.