For the vinaigrette combine all ingredients except the olive oil in a medium bowl. Using a whisk, stir the ingredients while drizzling in the olive oil to make an emulsion. Set aside.
In a small pot pour in the Abita Amber and bring to a simmer. Once it reaches a simmer, toss in the peeled and deveined shrimp. Slowly poach the shrimp until they are fully cooked; it takes about 6-8 minutes. Using a slotted spoon, remove the shrimp and place in a bowl of ice water (this keeps the shrimp from overcooking.)
To put the salad together, mix the vinaigrette with the mixed greens and place on a small plate. Place a few shrimp on the salad and garnish with the carrot and tomatoes.