Cook the white rice according to package directions. While it cooks, prepare the other components: slice the cucumber and scallions, and toast the sesame seeds in a dry pan over medium heat for 1-2 minutes until fragrant.
Pat the cubed chicken completely dry with paper towels and season with salt and pepper. This is crucial for achieving a good sear.
In a small bowl, whisk together the low-sodium soy sauce, mirin, brown sugar, minced garlic, and rice wine vinegar to create the sauce.
In a separate tiny bowl, mix the cornstarch with the cold water until smooth to create a slurry. Set both the sauce and the slurry aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat until shimmering. Carefully add the chicken in a single layer, ensuring not to overcrowd the pan (work in two batches if necessary). Cook for 2-3 minutes per side, undisturbed, until golden brown and cooked through.
Reduce the heat to medium-low. If you cooked in batches, return all the chicken to the skillet. Pour the prepared sauce mixture over the chicken.
Let the sauce bubble and simmer for 1-2 minutes, stirring to coat all the chicken pieces as it begins to reduce.
Give the cornstarch slurry a quick re-stir and pour it into the skillet. Continue to stir constantly for another 30-60 seconds until the sauce transforms into a thick, glossy glaze that clings to the chicken.
Remove the pan from the heat and stir in the toasted sesame oil.
To assemble, divide the fluffy rice among four bowls. Top with a generous serving of the garlic soy chicken, spooning any extra glaze from the pan over the top. Arrange the cucumber slices on the side and garnish with toasted sesame seeds and sliced scallions. Serve immediately.