Preheat oven to 350 degrees. In a glass bowl, toss 4 cups berries with 1/4 cup liqueur and brown rice syrup. Set aside.

Carefully place one sheet of phyllo on a work surface; keep remaining sheets between two damp towels to prevent drying out. Lightly spray sheet on work surface with cooking spray; cover with another sheet of dough. Repeat with two more sheets. Cut dough into six squares. Repeat entire process with remaining four sheets. (Extra phyllo dough can be wrapped tightly, sealed in a plastic bag, and frozen for future use.)

Tuck each phyllo square into a lightly greased muffin tin. Bake for 5–7 minutes, until golden. Remove and cool on a rack.

Place remaining 3 cups berries in a saucepan with ¼ cup water. Cook over medium heat until a saucelike consistency forms. Press through a fine-mesh sieve into a bowl. Discard pulp; transfer juice back to pan. Add 3 tablespoons liqueur and sugar. Cook until sugar dissolves, about 5 minutes. Spoon a little sauce into a small dish; stir in arrowroot until smooth. Return to pan and continue cooking and stirring until thickened, about 1 minute; adjust sweetness as desired. Remove from heat.

Spoon berry sauce into center of each dessert plate. Fill phyllo cups with berries and place on plates. Serve with additional sauce on the side.