Make the quick pickled red onions: Whisk the vinegar, sugar, and salt in a bowl until dissolved. Add the onion and toss to coat. Let onion sit at room temperature for at least 20 minutes and up to 1 hour, then cover and refrigerate until ready to use (for up to 2 weeks).
Make the green tahini sauce: In a large bowl whisk together the tahini, garlic, water, lemon juice, salt, and pepper. If it’s too thick, stir in additional water 1 teaspoon at a time until it’s the consistency of a thick salad dressing. Whisk in the parsley and set aside (or refrigerate in an airtight container for up to 1 week; bring to room temp and stir in a bit more water before using if necessary).
Make the grain bowl: Toss the rice in half of the dressing, then gently fold in the arugula. Add more dressing if desired, or reserve the rest for another use. Divide among 4 bowls, then toss with the radishes, avocado slices, sprouts, and half the pickled onions. Top with a poached or sunny egg.