Melt butter in a skillet over medium-high heat. Add the sliced onion and cook for 5 minutes. Mix in the salt and ground mustard.
Turn the heat down to medium-low and cook the onions for at least 30 minutes, stirring occasionally to avoid burning. If the onions look like they are getting too dark, add a tiny bit of water to the pan. Cook the onions until golden brown in color.
While the onions are cooking, preheat the air fryer to 400 degrees F.
Place the sausages in the air fryer and cook for 12-15 minutes, flipping halfway through. Pork sausages should be cooked to an internal temperature of 160 degrees F and chicken sausages to 165 degrees F.*
Take the brats out of the air fryer and let them rest for 5 minutes. Serve in hot dog buns topped with caramelized onions and spicy mustard.
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*NOTE: Precooked brats will be done in about 10 minutes and uncooked brats will take at least 15 minutes, possibly 20.
Nutritional information is based on third-party calculations and should be considered estimates. Actual nutritional content will vary with brands used, measuring methods, portion sizes and more.