Stir in ginger, garlic, and scallions; sauté 60 seconds. Add bok choy and cook, stirring often, until it wilts, about 2 minutes. Add remaining 1 teaspoon avocado oil and cauliflower rice. Cook, stirring occasionally, until rice begins to get tender, about 1 minute. Stir tamari mixture into skillet; cook, stirring occasionally and scraping up browned bits from bottom of skillet, until liquid cooks off and rice is tender, about 2 minutes.