1. Place garlic in the bowl of a mini food processor; process until finely chopped. Add nuts; process until a coarse butter forms. Add mayonnaise, 2 tablespoons water, and 1/8 teaspoon salt; process until smooth.
2. Combine 6 cups water and 2 1/2 tablespoons juice in a medium saucepan. Bring to a boil. Add artichoke hearts to pan; cook 6 minutes or until tender. Drain; dry with a paper towel.
3. Heat a large skillet over medium-high heat. Add oil to pan; swirl to coat. Add artichokes. Sprinkle with remaining 1/8 teaspoon salt; cook 2 minutes on each side or until well browned.
4. Combine remaining 1 1/2 teaspoons juice with arugula; toss to coat.
5. Spread 2 tablespoons hazelnut mixture on 1 side of each of 4 bread slices. Top hazelnut butter with 2 artichoke pieces, about 1/3 cup arugula mixture, 1/4 ounce sprouts, about 4 avocado slices, and 1 bread slice.