Preheat oven to 425 degrees F (220 degrees F). Line a baking sheet with grease-proof paper.
Slice the oranges very thinly (about 1/8-inch thick). Cut them in half again so that the orange slices look like half moons. Toss the orange slices with the olive oil and a small pinch of salt. Lay the orange slices in a single layer on the baking sheet, and bake for about 13-15 minutes. Make sure to rotate the baking sheet and flip the orange slices halfway to prevent them from burning too much. You want to be able to see some charring on the oranges.
While the oranges are baking, toss the sliced red onion with lemon juice, balsamic vinegar, and a pinch of salt. Set aside.
Prepare the vinaigrette by mixing all the ingredients together. Set aside.
When the oranges are roasted, toss them with the salad greens, onions, radish, pine nuts, basil and the vinaigrette. Fold in the avocados. Top with some freshly ground pepper.
Serve immediately.