Using a steamer insert, steam the sugar snap peas over high heat for 5 to 7 minutes or until just cooked. Transfer them to a bowl filled with ice and water to stop the cooking. Remove them from the bowl and put them on a paper towel to dry out.
Add potatoes to the same steamer. Steam potatoes over high heat until you can easily break them with a fork, about 20 to 25 minutes.
While the potatoes are cooking, in a small food processor or blender, process garlic with a healthy pinch of Kosher salt.
Add egg yolk, Dijon mustard and lemon juice. Process until smooth.
Add the extra virgin olive oil to a measuring cup. While the motor is running, slowly drip (not pour) the oil into the egg mixture until it begins to thicken. Gradually increase the oil to a thin steady stream, blending to a uniform creamy consistency. Season with salt. (If aioli breaks while blending, drizzle in a little lukewarm water a few drops at a time until consistency is reached again.)
Add the sugar snap peas and hot potatoes to a bowl and toss with aioli until well coated.
Cover and let sit at room temperature for an hour. If you’re making it more than an hour in advance, refrigerate it and bring it out a half hour before serving. Transfer the extra aioli to the refrigerator.
Just before serving, toss the sugar snap peas and potatoes with additional aioli and basil. Sprinkle the salad with flaky sea salt.
Notes
Don’t have sugar snap peas? No worries—this dish is still great without them.
If you're using larger potatoes you'll want to cut them into at least quarters.
You may have extra aioli. It’s great drizzled on grilled chicken or vegetables.
Aioli can be made a few days in advance and will keep for a week in the refrigerator.