Chicken Omurice (Japanese Chicken Fried Rice Omelette With Ketchup)

Name: Chicken Omurice (Japanese Chicken Fried Rice Omelette With Ketchup)
Total time: 30 min
Yield: 2
Ingredients: 2 cups cooked white sushi rice (12 ounces; 350g); see note; 5 tablespoons (75ml) vegetable or canola oil, divided; 1/2 cup minced yellow onion (100g; about 1/2 medium onion); 1/2 cup diced carrot (100g; about 1 large carrot); 3 ounces diced skinless, boneless chicken thigh (80g; about 1/2 cup); 1/4 cup ketchup (60ml), thinned with 1 tablespoon (15ml) water, plus more ketchup for serving; 1 scallion, thinly sliced; Kosher salt and freshly ground black pepper; 4 large eggs, beaten with a pinch of salt; Kewpie mayonnaise, for serving (optional; see note)