Heat oil in a 4-quart pot over medium heat. Add broccoli and onion and sauté for 3–4 minutes, until onions begin to soften. Add 2 teaspoons of minced garlic and cook for 1–2 more minutes, stirring occasionally, until the broccoli is nearly tender and onion begins to brown in some places.
Mix in non-dairy milk, 1 cup of vegan cheese, vegan beef crumbles, Tabasco sauce, Cajun seasoning, salt, and black pepper.
Reduce the heat to medium-low and simmer for 3–5 minutes, or until most liquids have been cooked down and the mixture is thick and creamy. Remove from the heat and set aside.
While the mixture is cooking, preheat the oven to 350°F.
Use your fingers to create a small hole on the side of each bread roll. Pull out the insides of the bread rolls and set them aside.
Once the cheesy broccoli mixture has cooled down enough to handle, add the remaining ½ cup vegan cheese and mix. Use a spoon to fill each hollowed-out bread roll with the filling. Use the removed insides of bread to plug the holes, then transfer stuffed rolls to a baking sheet.
Mix melted vegan butter and add the remaining ½ teaspoon of garlic, then brush the tops of the rolls with garlic butter. Bake for 10–12 minutes, or until the tops are golden brown and flaky and the garlic is toasted.