For the fried sage leaves: Heat a small saucepan with 1 inch oil over medium-high heat. Test the oil by touching the tip of a sage leaf in the oil; if it bubbles, the oil is ready for frying. Fry the leaves, 3 to 4 at a time, until the bubbles subside and the leaves become crisp. Drain on a paper-towel-lined plate and sprinkle with salt.
For the squash: Preheat the oven to 450 degrees F.
Using a chef's knife, cut off a small amount off the top and bottom of each squash. Set the squash, cut-side down, and cut in half. Using a large spoon, scoop out and discard the seeds. Cut each half into 5 wedges and place them in a large bowl. Add the olive oil, cayenne, cinnamon and 1 teaspoon salt. Toss with your hands to coat well, then transfer the squash to a rimmed baking sheet. Bake, flipping halfway through, until golden brown and fork tender, 35 minutes.
Place the butter in a small skillet and melt over medium heat until the foam subsides and the solids begin to smell nutty and turn brown, 3 to 4 minutes. Allow the butter to cool for 2 minutes. In a small bowl, whisk together the vinegar and sugar until the sugar is dissolved, then whisk in the brown butter, using a rubber spatula to get all the brown bits out of the pan. Season with 1/2 teaspoon salt. Lay the squash on a serving platter and spoon the vinaigrette over. Dollop with the mascarpone and sprinkle with the almonds and fried sage.