First, marinate the cooked Gigante beans and artichokes in the vinaigrette for marinade. Do this while they are still warm from cooking so they absorb the marinade as they cool. It is best to prepare these the day before so they fully take on the flavor of the marinade.
Toss the artichoke halves, roasted red pepper, basil leaves, feta cheese and Gigante beans together with 3/4-ounce of the vinaigrette. Season with a pinch of pepper, as the feta is already salty.
Place on a chilled dinner plate, making sure all elements are exposed, in a croissant- shaped mound, leaving the void on the plate at the two 'o clock position.
Dress the arugula with the remaining 1/4-ounce vinaigrette and place in a tight bundle in the void on the plate.
Garnish the edge of the salad with basil oil.
Toast sliced garlic in 2 tablespoons canola oil. Whisk together the toasted garlic and all other ingredients except the remaining oils. Slowly whisk the oil into the vinegar mixture to emulsify. Season with salt, pepper, sugar.