Preheat your oven to 475°F (245°C) with racks in the upper and lower third positions. Grease two baking sheets with 1 tablespoon of oil each along one short side; set aside.
Season the chicken with pepper, 1 1/2 teaspoons salt, and place it in a bowl. Add beaten eggs and stir to coat. Place flour in a shallow dish. In batches, dredge the chicken in flour, shaking off excess. Arrange the coated chicken on one side of each prepared baking sheet, spacing them out. Place sliced bell peppers on the other side, drizzle with remaining 2 tablespoons oil, and gently toss to coat.
Bake the chicken and bell peppers for about 15 minutes, rotating the baking sheets halfway through, until the chicken is browned in spots. Carefully flip the chicken using a spatula, then continue baking until it's crispy and reaches an internal temperature of 73°C (165°F) with a thermometer, about 5 more minutes.
Meanwhile, in a small saucepan, combine ketchup, pineapple juice, honey, soy sauce, rice vinegar, and remaining 1/4 teaspoon salt. Bring to a boil over medium heat, occasionally whisking. Reduce to medium-low and simmer, stirring frequently, until the mixture is reduced to 3/4 cup and coats the back of a spoon, about 5 minutes. Remove from heat.
Drizzle 1/4 cup of the prepared sauce over the cooked chicken on the baking sheets, tossing to coat evenly. Divide rice, chicken, and bell peppers among bowls. Drizzle remaining sauce on top. Serve immediately.
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