Finely grate 2 tsp. zest from the oranges and set the zest aside. With a sharp paring knife, slice the ends off the oranges. Stand each orange on one of its cut ends and pare off the rest of the peel in strips, making sure to remove all of the pith. Working over a small bowl, carefully cut the orange segments away from the connective membrane. Squeeze the membranes over the bowl to get any remaining juice.
Put the cumin seeds in a small, dry skillet and toast over medium heat until slightly browned and aromatic, about 1 minute. Remove from the skillet and let cool. Grind the seeds to a fine powder in a mortar and pestle or an electric spice mill.Using a mortar and pestle or the flat side of a chef’s knife, mash the garlic to a paste with a pinch of salt. Put the garlic paste and cumin powder in a small bowl (or keep it in the mortar) and whisk in the 2 tsp. orange zest, 3 Tbs. orange juice (from the bowl of orange segments), the lime juice, and the cayenne. Let the mixture sit for 5 to 10 minutes, and then whisk in the olive oil.
Meanwhile, peel the jícama and it cut into 1/8-inch-thick matchsticks 2 to 3 inches long. In a large bowl, combine the jícama, radishes, and scallions. Season with salt and pepper and toss with about two-thirds of the vinaigrette. Set aside for 5 to 10 minutes to let the flavors mingle.
Just before serving, thinly slice the avocados diagonally. Lay half of the avocado slices in a shallow bowl and season with salt and pepper. Drizzle some of the remaining vinaigrette on the avocado. Add the cilantro and orange segments to the bowl of jícama and toss gently. Taste and adjust the seasoning with more salt, pepper, and lime juice if needed. Put the jícama salad on top of the sliced avocado and tuck the remaining slices of avocado into the salad. Season the top slices with salt and drizzle with the remaining vinaigrette. Serve immediately.