Fill a medium bowl with ice cubes and water and set it next to the stove.

Fill a small saucepan about three-fourths full of water. Bring the water to boil over medium-high heat. Add the basil and cook for 10 seconds. Using a slotted spoon, immediately transfer the basil to the bowl of ice water and let cool for 5 minutes. Using the slotted spoon, remove the basil from the ice water, wrap the wilted basil in a paper towel, and squeeze to wring out as much water as possible.

Place the blanched basil, the shallot, garlic, lime juice, vinegar, olive oil, and red pepper flakes in the bowl of a small food processor fitted with the multipurpose blade. Blend until well combined and smooth. Season to taste with salt and refrigerate in a tightly closed mason jar for up to 4 days.