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1
Peel the potatoes, and slice them about 1/4-inch thick. Lay them in the middle of a clean, cotton dish towel, and jumble the pieces around a bit. Fold the towel snugly around the potatoes, overlapping all the edges to make a burrito-like bundle.
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2
Microwave the bundle in 60-second increments, turning and flipping the bundle and shaking it around a bit after each cycle, until the potatoes become transluscent. This should take 3 to 4 minutes. The potatoes should be tender, but not soft. Take care handling the hot bundle and the steam that will come out when you open it.
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3
Heat the oven to 400u00b0 F. Heat the olive oil in a 10-inch oven-proof skillet over medium-high heat. Carefully add in the onions and potatoes and cook until the onions are soft, stirring frequently, about 5 to 7 minutes. Neither the onions nor the potatoes should be browned, but just softened. Adjust the heat as necessary.
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4
Beat the eggs and cream (if using) and pour them into the pan. Pull back the edges of the omelet to allow the egg to run to the bottom of the pan (a rubber or silicone spatula works well for this). Repeat around the edges until you've gone all the way around the omelet a couple of times and the bottom begins to firm up, about 5 minutes.
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5
Sprinkle the top with salt and pepper. Place the pan in the oven and cook the omelet until just set, about 8 to 10 minutes. Take care not to overcook; the top can still look a little shiny with egg and should not be brown.
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6
Remove from the oven and allow to cool to room temperature.
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7
To prepare the sandwiches, slice the baguette into four equal lengths, then slice those pieces lenghtwise.
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8
Cut the tomatoes at their equators; on the bottom half of the baguette, smush the cut-side of the tomato, squeezing out the juice, seeds, and some of the flesh onto the bread. Top with slices of omelet. On the top half of the baguette, spread some allioli. Assemble the sandwich, wrap in up in some wax paper, and pretend you're in Spain. Unless you actually are in Spain, in which case, yay for you!
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9
Place the egg yolk in a tall measuring cup or tumbler with the garlic and a splash of the olive oil. Using an immersion blender, begin to blend the ingredients for a few seconds, until they are mixed. Add in another splash of oil and mix again. Continue adding in oil a bit at a time until about half of it is incorporated. From there, you can pour in bigger splashes of oil so long as you are making sure it is completely emulsified before adding in the next splash. At this point, you'll need to move the blender in a slight up and down motion to be sure everything is being incorporated, but you also want to be careful not to overbeat the mixture.
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10
Finally, add in the salt and lemon juice and blend just to combine. Store covered in the refrigerator until ready to use.
