Place all of the dressing ingredients in a food processor bowl. Pulse a few times to mince the basil leaves and shallots. Place in the refrigerator for at least 30 minutes to allow the dressing to thicken and flavors to blend.
In a medium bowl toss the spring mix, cucumber, radishes, and green pepper. Divide into 2 serving bowls. Split the avocado and feta between the 2 bowls.