Preheat oven to 375° F.
Heat the oil in a non-stick sauté pan over medium heat.
Once the oil is hot, pan-fry the hot dogs for 6 to 7 minutes, until they begin to brown a bit, rolling them around as they cook to ensure they cook evenly on all sides.
Remove the hot dogs from the pan and cut each dog into 3 even pieces; you will have 12 pieces altogether.
To prepare the mini chili cheese dogs, place the dinner rolls in a 9 by 13-inch or 3-quart baking dish, leaving them attached.
Using a sharp paring knife, cut a small square in the middle of each roll, leaving about a 1⁄2-inch border around the edges. Do not cut all the way through.
Gently press down on the cut-out square to form an opening in the middle of each roll.
In a small bowl, mix the softened butter, parsley, and garlic powder, then brush the rolls with the mixture.
Sprinkle 1 cup of the vegan cheddar shreds into the bottoms of the hollowed-out rolls, then insert a piece of hot dog into each one.
Next, fill each roll with a couple tablespoons of the chili, then sprinkle the remaining ½ cup of cheddar shreds over the top of the rolls.
Cover loosely with foil and bake until the cheese has mostly melted, 15 to 20 minutes.
Remove the foil and bake another 5 to 10 minutes, until the chili is bubbly and starts to brown. Remove and let cool for 5 minutes.
Garnish with vegan sour cream and green onion and enjoy!