Pierce potatoes in several places with fork.
Melt butter in heavy large skillet over medium heat.
Add potatoes and season with salt and pepper.
Cover and cook until potatoes are almost tender, shaking skillet occasionally, about 25 minutes.
Add 2 tablespoons basil, shallots and garlic.
Reduce heat to medium-low; cover and cook until potatoes are golden brown and very tender, shaking skillet occasionally, about 10 minutes longer.
Season with additional salt and pepper.
Transfer to bowl.
Sprinkle with remaining 2 tablespoons basil.
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