Heat the butter in a saucepan over medium heat and add the sliced onions, followed by the sea salt. Stir to coat, place a lid on the pan, and cook over medium to low heat for about 15 minutes until softened and beginning to release their moisture.
Remove the lid, reduce the heat slightly, and continue cooking until the onions turn a deep amber color. Stir every five minutes to ensure the natural sugars caramelize without burning. This process will take about 50 minutes in total and you will notice the onions becoming richly sweet and fragrant as they deepen in color.
Remove the casing from the black pudding and break it into smaller pieces. Prep the others ingeredients as well.
After removing the caramelized onions from the pan and setting them aside, increase the heat to medium to low and add the olive oil without washing the pan. Add the parsley, habanero pepper, scallions, thyme leaves, and black pepper. Cook for about 3 minutes until you hear the gentle sizzle and the aroma of the herbs and pepper fills the kitchen.
Add the black pudding to the pan and crush it as you stir, combining all the flavors into a somewhat thick, paste-like consistency.
After 3 to 4 minutes, fold in the caramelized onions and heat through for about 2 minutes.
Serve warm as a topping for sandwiches or crackers. Alternatively, keep the caramelized onions separate and spoon them over the finished pudding as a topping.
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