A bright salad of crisp lettuces and an assertive vinaigrette is the ideal accompaniment for this rich vegetarian gratin.
Preheat oven to 425 degrees; butter a 10-inch, 1 1/2-quart gratin dish. In a skillet, cook 2 tablespoons butter, leeks, and a pinch of salt over medium-high heat, stirring, until soft, 8 minutes. Add vermouth; cook until mostly evaporated, 1 to 2 minutes. In another pan, melt remaining butter. Toss with panko; season with salt and pepper.
Scatter half of pasta, leeks, squash, and cheese in gratin dish. Season with salt and pepper; repeat with remaining half of each. Pour broth and cream evenly over top; cover with parchment-lined foil and bake until squash is tender, 25 minutes. Sprinkle panko mixture over gratin. Bake, uncovered, until golden and bubbly, 20 to 25 minutes. Let cool 10 minutes; serve with greens.
For easy prep, place Brie in the freezer for 10 minutes until firm, then cut into small pieces.