Preheat the oven to 425 degrees F. Line a baking sheet with foil and coat with cooking spray. Combine the orange slices, 2 tablespoons maple syrup and the brown sugar in a medium bowl. Arrange the orange slices on the baking sheet in a single layer; bake, flipping once, until they are glossy and start blackening around the edges, about 15 minutes. Let cool.
Combine the bourbon, vermouth, the remaining 1 tablespoon maple syrup and the bitters in a cocktail shaker; fill with ice. Shake well and strain into a cocktail glass; garnish with blackened orange slice.