Blue Hill Stone Barns private table?
I have done the kitchen table experience twice and both times have been amazing experiences - in fact I would say they are my two best meals ever. With the kitchen table you spend a majority of the meal dining literally inside the kitchen, but they do move you around some. When we did this during a warm time of year we started with cocktails and canapes outdoors, had the savory courses in the kitchen and for dessert were led to what was an old manure barn (likely what you are referring to as the shed); they had it beautifully lit with tons of candles and it was such a romantic, intimate experience. Outside of those dining at the kitchen table I am not sure who else receives this experience or if they try to accommodate requests.
When we recently did the kitchen for a second time (with the weather considerably colder) we started with cocktails at the bar area, had the canapes and most savories in the kitchen, for the final savory were moved to an enclosed room off the dining room with floor to ceiling windows looking outdoors - again lit with candles, they then took us outside for s'mores and then back to the kitchen for the dessert courses.
The kitchen table experience is pricier than the standard meal, but is such an incredible, memorable, unique experience I strongly recommend partaking. Both times the assistant general manager was our personal server for the night but we also had lots of interaction with the wine director and the chefs. Everybody we encountered were wonderful people and they really try to customize the experience to the individuals. You can do the kitchen table with a party of 2 to 4 people.
I don't know about a "shed". I do know that they had been offering a 4 seat private in kitchen dining experience with the chef where you watch it all happen and the chef is essentially your server. I was going to "gift" it to my nephew for his bar mitzvah b/c he is soooo into cooking.
I know quite know how readily available this is, or if they decided to continue with it as I had asked in May/June .