Make the aioli: Place the saffron in a skillet and bring to medium-high heat. Gently toast until the skillet is too hot for you to touch the center with your finger, about 1–2 minutes.
Transfer the saffron to a mortar and pestle, and grind it into a fine powder.
Pour 3 tbsp. of slightly warm water into the mortar. Set aside.
Place the egg yolk in a medium bowl and add a pinch of salt. Whisk the yolk and start to drizzle the olive oil in very slowly. The yolk and the olive oil will start emulsifying. Continue to whisk vigorously. When it starts to get thick, pour a very small amount of the saffron liquid into the aioli to soften it and continue whisking. Keep adding olive oil until it thickens again. Add more saffron water to your liking.
Make the salad: Preheat the oven to 400°F.
Wash the beets well. Place the beets in a small ovenproof dish with 1 cup water, bay leaves, and 1 tsp. olive oil. Cover with foil and roast until the beets are soft when you put a knife through them, about 1 1⁄2 hours.
In the meantime, prepare the vinaigrette. Place the diced shallot in a small bowl and pour vinegar over top. Season to taste with salt and pepper, and let it sit for 10 minutes. Add 1/2 cup olive oil and whisk thoroughly to combine.
Tear the leaves of the radicchio into bite-size pieces. Place in a large serving bowl and transfer to the refrigerator until ready to assemble.
When the beets are cool enough to handle, peel and cut into 1⁄2-inch cubes.
Place the beets in a small bowl with 1⁄2 cup olive oil. Add orange slices, and season with salt and pepper.
Whisk the vinaigrette well and toss with the radicchio. Top with the beets. Drizzle with saffron aioli and serve.