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Dice the tomatoes and onions. Mince the garlic cloves. Mince the dill, remove the stems from the oregano and mince the leaves, and remove the stems from the thyme.
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Rinse the lentils thoroughly under cool water and make sure there are no small stones or debris.
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Place the lentils, tomatoes, onions, garlic, herbs into the slow cooker. Pour in the Worcestershire sauce, tomato puree, beer, broth, bay leaves, salt, and black pepper as well.
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Turn the slow cooker to high and allow it to cook, with the lid on, for about 5 hours or until the liquid has been absorbed by the lentils and they have become thick but not dry.
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Heat the oil in a saute pan over medium-high heat. Add the vegetarian sausages to the pan and allow them to cook, turning so they can brown on each side, for about 6-8 minutes. They will be plump and browned when they are ready. Turn off the heat.
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Cut the hoagie rolls down the side, but not all the way through so that one side stays attached. Open them and set them aside.
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Spread mayonnaise on the inside of each bun before adding the hot dogs and topping with the lentil chili.
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Add cheese, diced onion, and Dijon mustard on top of each hot dog before serving