Looking for a single, good opening that revolves around a “crab” pawn structure I have often heard (or this one video just got it stuck in my head) Youtube videos (the timestamp is 2:37, nothing else relevant) refer to this kind of pawn structure as a “crab” pawn structure (below, white pawns.) The name makes sense because it is like a crab pincer enclosing the board, as agadmator said.
This is just an example; it is not to be analyzed.
[FEN &quot;&quot;]
[startply &quot;8&quot;]

1. e3 f5 2. f4 Nf6 3. c4 c5 4. d3 Nc6

Is there a good opening that revolves around such a “crab” pawn structure? I seek merely one, not all possible ones. As long as the structure of the pawns, as shown in the example, is the same, the “crab” can be anywhere on the board.
I would like to utilize such an unorthodox playing method to surprise opponents. I would like to know the advantages/disadvantages of the opening, such as how to counter/play it. There is no need to cover all possible variations.
To answer your question, there are no good openings that revolve around this "crab" pawn structure. This is because this structure takes a lot of pawn moves, decreases the mobility of your bishops, and creates weakness on the kingside. It would even be difficult to come up with a respectable variation of any opening that has this pawn structure (perhaps the variation in the link provided is playable, but I don't think it gives an objective advantage). 
Of course the pawn structure in the link is different than the one you displayed. Either way, I recommend avoiding these "crab" structures at all costs. 
If you want to surprise you're opponent with unorthodox openings in an aggressive manner, try some gambits out. For example, King's Gambit, Smith Morra Gambit, Evans Gambit, etc.