Preheat the oven to 425 degrees F.
Make the jam: Combine the onion, butter and salt in a small saucepan with a lid. Sauté over medium-low heat, covered, for 20 minutes, stirring occasionally. Uncover, add the wine and vinegar and continue to cook over medium heat, stirring slightly more frequently, until there is no liquid left and the onions are soft and caramelized, about 20 minutes. Remove from the heat and stir in 1 tablespoon of Grana Padano.
Starting at the stem end, cut the figs partially in half, leaving the bottom end intact.
Carefully tear each strip of prosciutto in half lengthwise and set aside.
Fill each fig with 1 heaping teaspoon of red onion jam, then wrap the bottom half of the fig with a strip of prosciutto so you get a tight little package. Secure with a toothpick horizontally through the middle. I used longer skewers and did them in pairs.
Arrange in an even layer on a parchment-lined baking sheet and sprinkle with the remaining cheese so it adheres to the red onion jam. Roast in the oven for about 10 minutes, or until the prosciutto is crispy and the cheese is lightly browned.
Serve immediately, warm, over a bed or arugula for garnish.