You will need 6 small, straight sided glasses, at least 6 oz. each. In a medium bowl, stir together Parmesan Peppercorn spread and half-and-half until blended. Set aside.
Rinse finely chopped shallot in a small strainer; drain well and place in a large bowl. Add lemon juice, olive oil, salt and pepper. Whisk together to combine. Halve, pit and peel avocados; mash until smooth and add to bowl.
Divide the smoked salmon and capers between the 6 glasses. Then layer each with avocado mixture and cheese spread. Garnish with dill sprigs or lemon twist.