In a medium bowl, whisk together the olive oil, grapefruit juice, champagne vinegar and garlic until the mixture emulsifies. Season to taste with salt and pepper. Set aside. You may have to whisk again before serving.
For the shrimp:
Season the shrimp with cayenne, salt and pepper. Heat a large sauté pan over medium heat, add the olive oil and heat through. Add the butter and allow to melt then add the shrimp to the pan. Sauté, turning once until the shrimp are no longer grey and opaque and just cooked through, about 3 minutes. Remove to a bowl and set aside.
For the salad:
Heat a grill or griddle pan over medium-high heat. Halve the avocado and remove the pit. Brush the avocado with the olive oil and place, cut side down, on the grill or griddle pan and cook, unmoved until grill marks develop, about 2 minutes. Season with salt and set aside.
Add the arugula and fennel and grapefruit to a large mixing bowl. Add 3 tablespoons of the dressing (add more if necessary) and toss to combine. Slice the avocado and add to the bowl. Toss to combine and top with the shrimp. Serve immediately.