Melt butter in a heavy large saucepan over medium-high heat.

Add chopped onion and thinly sliced garlic; saute until golden, about 5 minutes.

Add 3/4 cup bourbon; boil until most of liquid is absorbed, 6 to 8 minutes.

Whisk in 1/4 cup bourbon, ketchup, hot pepper sauce, tomato paste, and brown sugar.

Bring to a boil. Reduce heat and simmer until sauce thickens slightly, stirring occasionally, about 10 minutes.

Season marinade with salt and pepper to taste.

Remove marinade from heat and allow to cool to room temperature.

Place chicken drumettes in a 15x10x2-inch glass baking dish.

Pour marinade over chicken drumettes, ensuring they are well coated.

Cover the dish and refrigerate overnight to marinate.

Preheat oven to 375°F (190°C).

Line a baking sheet with foil or parchment paper.

Place a cooling rack atop the prepared baking sheet.

Arrange the marinated chicken drumettes on the rack, spacing them slightly apart.

Spread any remaining marinade from the dish over the drumettes.

Sprinkle with salt and pepper.

Bake the drumettes (still on cooling rack) until cooked through and brown in spots, about 45 minutes.

Transfer the baked drumettes to a serving platter.

Serve the chicken drumettes with Blue Cheese Dipping Sauce alongside.