Apple Croustade (Flaky Apple Tart)

Melt 4 tbsp. butter in a 4-qt. saucepan over medium-high heat. Add 1⁄2 cup granulated sugar, salt, and apples; cook, stirring occasionally, until apples are slightly caramelized, about 20 minutes. Pull pan from heat and add armagnac; carefully ignite with a match. Return to heat and cook until flames subside and liquid is reduced by half, about 3 minutes; let cool.

Assemble and bake the tart: Heat oven to 425°. Grease a 10" springform pan with butter; set aside. Melt remaining butter in a 1-qt. saucepan; keep warm. Lay 1 sheet phyllo on a work surface; brush with some melted butter and sprinkle with 1 tsp. granulated sugar. Fit into prepared pan, allowing corners of dough to hang over edges. Repeat using 3 more sheets phyllo, laying each sheet at a 45° turn from the last. Spread apples over dough in an even layer. Cut remaining sheets of phyllo in quarters, and, working with 1 piece at a time, pinch at the center and flip over, so that the corners are pulled together and facing up; place over top of tart. Repeat with remaining pieces phyllo until top of tart is covered. Drizzle with remaining melted butter; bake until golden and crisp, about 30 minutes. Let tart cool completely in pan, then unmold and transfer to a serving platter.