Steam potatoes for 10-12 minutes, or until tender.
Heat olive oil over medium heat in a 10-inch skillet, either non-stick or very well seasoned cast iron. Add shallots and chorizo and saute for 7-8 minutes.
Break eggs into a medium bowl. Whisk them together with chicken broth, salt, 1 tbsp of parsley, and about half the scallions.
Add potatoes to skillet and mix them well with the shallots and chorizo. Pour in egg mixture and stir everything together, shaking the pan a bit to get the top of the tortilla fairly even.
Reduce heat to medium-low, and cook the tortilla, running a knife along the edge occasionally to let some of egg run down along the inside edge of the skillet, until it is set most of the way through, 8-10 minutes. The top will still be wet.
At this point you have a choice. You can turn the heat all the way to low, cover the skillet, and let it finish, about 5 minutes. Or you can flip the tortilla by inverting it onto a plate and then sliding it into the pan again with a little more olive oil, cooking it another 3-4 minutes. I have used both methods and they both make a tasty tortilla. Method one is simpler and method two gives you crispy top and bottom.
Once the tortilla is cooked and set all the way through, loosen it from the skillet if needed and then slide it out onto a cutting board or serving dish. Serve warm or at room temperature with the aioli. Cut it into wedges for dinner portions or into squares for tapas portions.
For the aioli: In a medium bowl, whisk together the egg yolk, salt, and 1 tbsp of the lemon juice. The yolk will get light colored and then darken a bit. Now is the time to start adding the oil. Whisking the egg mixture constantly, begin adding the oil in a slow, steady stream until all the oil is used and the sauce has thickened.