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1
Place all of the ingredients in a large bowl and mix with your hands until evenly combined.
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2
Cover with plastic wrap and refrigerate until the flavors meld, at least 4 hours and up to 24 hours.
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3
When the sausage is done marinating, heat the measured oil in a large frying pan over medium-low heat until shimmering.
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4
Add the peppers, onions, garlic, and red pepper flakes.
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5
Season with salt and pepper and cook, stirring occasionally, until softened, about 20 minutes.
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6
Cover with a tightfitting lid to keep warm and set aside while you cook the sausage patties.
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7
Divide the venison sausage into 6 equal portions.
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8
Shape each portion into a thin, rectangular patty slightly larger than the hoagie rolls; set aside.
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9
Heat a grill pan or outdoor grill to medium (about 350 degrees F to 450 degrees F).
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10
When the grill is ready, use tongs to rub the pan or grate with several layers of paper towels dipped in olive oil.
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11
Place the sausage patties on the grill, cover the grill, and cook the patties undisturbed ( press down on them) until grill marks appear on the bottom, about 2 to 3 minutes.
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12
Using a spatula, flip the patties and divide the cheese among them.
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13
Cover the grill and continue cooking until the cheese is melted and the patties are just slightly pink in the center for medium (about 140 degrees F to 145 degrees F on an instant-read thermometer), about 2 minutes more.
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14
Remove to a clean plate and let rest in a warm place or tent loosely with foil.
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15
Meanwhile, toast the rolls.
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16
When the rolls are ready, place 1 patty on each roll, evenly divide the onion-pepper mixture over the patties, and serve.