Rinse and cook rice according to package directions; cover off heat for 5 minutes, then fluff.
Heat oven to 425°F (220°C). Line a rimmed sheet pan with parchment. Toss eggplant with neutral oil and kosher salt; spread in one layer and roast 18 minutes, turning once halfway.
Whisk white miso, soy sauce, rice vinegar, maple syrup, sesame oil and warm water until smooth. Brush or toss the eggplant with the glaze and roast 8 to 10 minutes more, checking early so the maple does not scorch.
Toss cucumber with 1 teaspoon rice vinegar and a pinch of salt. Divide rice among bowls, add glazed eggplant and cucumber, and finish with sesame seeds and scallions.