In a small bowl, whisk vinegar, mustard, honey, salt, and pepper until combined. While whisking, slowly stream in oil until a smooth, shiny dressing forms.

Transfer dressing to an airtight container and refrigerate until ready to use.

Make Ahead: Dressing can be made 5 days ahead. Keep refrigerated.

Pour rice into a fine-mesh sieve. Rinse under cold water, mixing with one hand until water runs clear, about 1 minute.

Fill a small pot with 1 ½ cups cold water and bring to a boil over high heat. Stir in rice and ¾ teaspoon salt. Return to a boil, then reduce heat to medium-low. Cover and simmer until rice is tender and water is absorbed, about 45 minutes. Remove from heat, uncover, then cover pot with a paper towel. Place lid over paper towel and let sit 15 minutes more.

Meanwhile, arrange racks in upper and lower thirds of oven; preheat to 425°. Line 2 baking sheets with foil. In a small bowl, combine onion powder, garlic powder, paprika, and 2 teaspoons salt.

On one prepared sheet, rub chicken with 1 tablespoon oil; season with 1 ½ teaspoons seasoning mix. On second prepared sheet, toss potatoes with remaining 2 tablespoons oil; season with remaining seasoning mix and spread in a single layer.

Roast chicken on lower rack and potatoes on upper rack until chicken is cooked through and an instant-read thermometer inserted into thickest part registers 160°, 15 to 20 minutes. Let chicken rest on baking sheet at least 10 minutes, then transfer to a cutting board and cut into ½" cubes. Wipe off sheet.

Meanwhile, continue to roast potatoes until tender and lightly browned, 5 to 10 minutes more. Let cool on baking sheet.

Reduce oven temperature to 350°. Spread almonds on clean baking sheet and roast until golden brown, 8 to 10 minutes. Let cool, then coarsely chop.

In a large bowl, combine kale with remaining 1 teaspoon salt. With clean fingers, massage salt into kale until kale softens and slightly darkens, about 1 minute.

Divide kale among 4 bowls. Top each bowl with chicken, potatoes, rice, apple, cheese, and almonds. Drizzle with dressing.

Make Ahead: Chicken, potatoes, rice, and almonds can be prepared 3 days ahead. Store in separate airtight containers and refrigerate.