Cook rice according to package directions with a large pinch of salt, then let cool and pack into airtight container. Meanwhile, combine vinegar, soy, and honey in a small sauce pot. Bring to boil, then simmer over medium-high heat until reduced by half, about 10 minutes. Set aside.
Heat oil in a large skillet over medium-high heat until shimmering, then add eggplant, sprinkle with 1/4 teaspoon salt, and cook, stirring occasionally, until it begins to shrivel and char (10 to 12 minutes). Add sugar-snap peas and saute until bright green, about 2 minutes longer. Pour in reduced sauce and toss over medium heat until vegetables are well coated, 1 minute. Pour on top of the rice in the airtight container. Let cool to room temperature, stir in basil, then refrigerate until ready to eat. Eat cold or microwave covered with damp paper towel to reheat.