Preheat the oven to 375º and line a baking sheet with parchment paper.
Open the canisters of crescent dough, and slice each of the crescent triangles into smaller triangles. Each of the pull-apart crescent rolls should yield 6 smaller triangles. Set aside.
Pat dry the mini cocktail franks and begin placing the hot dogs ¾ of the way down of each smaller triangle.Roll inward to wrap the hot dog in the crescent roll dough.
Place on the baking sheet and repeat these steps until all of the hot dogs are used. If there's crescent dough left over, feel free to freeze or use as desired.
In a microwave-safe dish, melt the butter then add in the minced garlic. Spoon a little of the garlic butter mixture on top of each of the mini hot dogs and top with fresh basil.