Whisk together the soy sauce, Shaoxing wine, gochujang, honey, sesame oil, garlic and reserved kimchi liquid in a medium bowl until combined. Measure out 1/2 cup of the soy marinade and reserve it for the rice.
Add the shrimp to the bowl with the remaining marinade and toss until completely coated. (If time allows, let sit uncovered at room temperature for 30 minutes to let the marinade penetrate.) Drain through a medium-mesh strainer, discard the marinade and return the shrimp to the bowl.
Heat 2 tablespoons of the vegetable oil in a large nonstick skillet over high heat until it shimmers and tiny wisps of smoke are visible. Add the shrimp in a single layer and cook, flipping once, until browned on both sides, about 1 minute per side. Transfer to a large bowl.
Heat 1 tablespoon of the vegetable oil in the same skillet over high heat and cook the onions until translucent and just tender, stirring often, about 2 minutes. Add 1/3 cup of the reserved marinade and cook, stirring occasionally, until the liquid has almost evaporated, 1 to 2 minutes. Transfer the onion mixture to the bowl with the shrimp.
Heat 2 tablespoons of the vegetable oil in the same skillet over high heat and cook the kimchi, tossing often, until most of the liquid has evaporated and the kimchi is lightly browned in spots, about 2 minutes. Add the basil and toss to wilt. Transfer to the bowl with the shrimp.
Heat 1 tablespoon of the vegetable oil in the same skillet over high heat. Add the beaten eggs and cook, stirring vigorously, for 10 seconds (no, really, 10 seconds). Transfer to the bowl with the shrimp and break up the eggs into 1-inch pieces.
Heat the remaining 2 tablespoons vegetable oil in the same skillet over high heat. Add the rice, patting it down into an even layer and breaking up any clumps, and let fry undisturbed for 1 minute. Vigorously toss, breaking up any clumps, until the grains have dried out, separated and start to crisp and lightly brown, about 3 minutes.
Add the shrimp mixture to the rice and vigorously toss (or stir) until completely combined and the shrimp mixture is evenly distributed throughout the rice. Season with the remaining soy marinade if necessary, adding 1 tablespoon at a time and tossing well to combine, until seasoned as desired.
Top the fried rice with the scallions before serving.