Melt butter in 4-quart saucepan over medium heat; add shallots, fennel, celery, and leeks, and sauté until tender.
Stir in the Chardonnay and tarragon stalks, increase heat to medium-high, and simmer for about 15 minutes or until reduced by ¾. Add the cream and simmer for about 10 minutes or until reduced by ⅓.
Strain sauce through a sieve into a 2-quart saucepan. Return to stove over medium heat. Mix butter and flour in small bowl; stir into cream sauce and simmer for 5 to 6 minutes to thicken.
Add Gruyère, cheddar, and Parmesan and simmer for 10 minutes, stirring constantly, or until it reaches a consistency of a thick cream. (Sauce thickens more as it cools.)
Cut lobster into bite-sized pieces.
Heat wine in medium saucepan with steamer insert, over medium-high heat until boiling. Reduce heat so that wine simmers; add lobster to steamer basket, cover and cook about 3 to 5 minutes or until lobster changes from translucent to white; remove from heat, setting aside ¼ cup for garnish.
Preheat oven to 300°F. Place 1 tablespoon Parmesan on baking sheet lined with parchment paper; lightly shape into an oval. Repeat with remaining cheese, spacing about ½ inch apart.
Bake 10 minutes or until golden and crisp. Cool.
Cut tarragon leaves into thin strips. Stir together rigatoni and cheese sauce, coating evenly. Fold in lobster, reserving ¼ cup for garnish. Season to taste with salt and pepper. Garnish with tarragon, lobster, and Parmesan crisps; serve immediately.
