Heat oil in a 10-in. nonstick skillet over medium. Cook plantains until golden brown, about 2 minutes per side. Transfer to a paper-towel-lined plate and let cool slightly, about 5 minutes. Sprinkle with 1/4 tsp. salt. Wipe skillet clean.
Stir together beaten eggs and 1/4 tsp. salt in the same skillet over medium-low heat. Cook, stirring occasionally, until large curds form and eggs are mostly set, 3 to 4 minutes. Remove from heat.
Combine beans, 1/4 cup pico de gallo, and remaining 1/2 tsp. salt in a medium microwavable bowl. Cover with plastic wrap and microwave on high until hot, 1 to 2 minutes. Divide rice, bean mixture, plantains, eggs, avocado, sour cream, and remaining 1/2 cup pico de gallo among 4 serving bowls.
Allowing picky eaters to assemble their own meals gives them a feeling of independence and makes it more likely that they will try new foods.