Chicken Potpie With Phyllo Clusters

Place chicken in a medium Dutch oven or large saucepan, skin-sides down. Cover with broth and 2 cups water; add 1 teaspoon salt. Bring to a boil, then reduce heat to low and simmer, uncovered, until chicken is just cooked through, about 20 minutes. Transfer chicken to a plate; let cool about 30 minutes. Strain broth, discarding solids (you should have about 3 1/2 cups).

Remove chicken from bones and shred meat into bite-size chunks. Discard skin and bones. You'll need 2 1/2 cups chicken; save the rest for salads or sandwiches.

Wash and dry Dutch oven or saucepan; melt butter in it over medium-high heat. Add leeks, carrots, celery, potato, 1 teaspoon salt, and some pepper. Cook, stirring, until leeks are translucent, about 4 minutes. Add vermouth; cook until mostly evaporated, about 1 1/2 minutes.

Stir in flour; cook 20 seconds, stirring constantly. Stir in 2 3/4 cups broth. Bring to a boil, then reduce heat and simmer, stirring often, until potato is just barely tender, about 5 minutes (mixture will look very thick; that's okay, as the vegetables will release liquid in the oven).

Stir in chicken, peas, artichokes, and chopped tarragon. Season to taste; transfer to a 2 1/2-quart baking dish (such as a 9 1/2-to-10-by-2-inch-deep round one) and let cool 30 minutes, or refrigerate, covered, up to 1 day.

Preheat oven to 375°F. Brush a sheet of phyllo lightly with melted butter. Scrunch into a loose ball and place on filling. Repeat with more sheets brushed with butter, covering the filling but leaving a bit of space between pieces. Bake until golden brown and bubbling in center, 45 to 50 minutes. Let cool 20 minutes before serving, garnished with tarragon sprig.