It depends on what your exact requirements are.
If you can live with something which tastes like butter+espresso, but is softer, pick an emulsifier, add it to the double shot of espresso, and then knead the butter into it. Assuming that by "block of butter" you mean 250 g of butter, and by a "double shot of espresso" you mean 50 ml, the result should be still well spreadable in texture, not too liquid. You should be able to smear it on a slice of bread, or pipe it with a bag. The choice of emulsifier depends mostly on your personal preference for the final texture and added taste notes, so it makes no sense to ask "which one" - you will have to test them until you find one that's good enough for you.
If you have even more leeway in your requirements on texture and taste, you can also pick a recipe for coffee-flavored buttercream and use that. You will still have the combination of coffee taste and butter taste, but also a decent bit of sugar, and also as a foam, the taste will be different from simply "a block of butter with coffee". It is a great choice for patisserie though, and more readily available to home cooks than any of the other methods I mention.
If you absolutely need exact butter texture, the problem gets much more complicated. The easiest way would be to dissolve instant coffee in as little water as possible and knead into the butter. If that's not good enough for you, the second easiest (and this is not a joke) is to churn your own butter, adding the coffee before starting the churning (it will be worth experimenting with brewing the coffee directly in cream or milk instead of water). Anything else will require you to get well acquainted with the theory and practice of doing chemical extractions, so expect to have to read a few books and buy some exotic hardware before you can develop a process for that.