Preheat the broiler to high.
Combine the sugar and Champagne vinegar in a small saucepan. Bring to a simmer over medium heat; cook until the sugar is fully dissolved and the mixture has thickened just slightly, 3 minutes. Remove from the heat and stir in the dried cranberries. Let sit for 10 minutes to plump the cranberries.
Meanwhile, on a rimmed baking sheet, combine the sliced Brussels sprouts, 2 tablespoons of the olive oil, 3/4 teaspoon of the salt, and the pepper flakes. Toss well to coat. Broil for 6 minutes, stirring halfway through and rotating the baking sheet as needed for even browning. Add the sprouts to a medium bowl and toss with the cranberry mixture while hot. Set aside for 5 minutes to let the flavors marry.
In a small bowl, whisk the remaining 2 tablespoons olive oil and 1/4 teaspoon salt into the ricotta. Using a small offset spatula, spread the crostini with the ricotta mixture. Top each crostini with a spoonful of the Brussel sprout mixture and sprinkle with a few pine nuts.
To make the crostini, brush twenty-four 1/4-inch-thick baguette slices with 1/4 cup extra-virgin olive oil, and sprinkle with a 1/4 teaspoon salt. Bake in a 400-degree oven for about 5 minutes, rotating halfway through.
Recipe courtesy of Giada De Laurentiis