Preheat oven to 400 degrees.
Cut butternut squash down the middle, lengthwise. Remove seeds, then cut each half into 3 equal pieces (you’ll have 6 pieces total).
In a large bowl, combine the melted butter and brown sugar. Toss with the acorn squash pieces, then add salt and pepper. Toss again.
Lay out the pieces on a foil rimmed baking sheet skin side down. Place in oven for 35-40 minutes, or until squash is fork tender. Remove and brush with more melted butter if you desire.
In a separate bowl, toss together arugula, olive oil, chèvre, and dried cranberries. Place on your serving dish and top with the roasted squash pieces. Drizzle with aged balsamic (optional).