I’ve just stumbled onto the concept of compound butter and so far I’m loving it. I’ve experimented with lemon and orange zest as well as thyme and dill.
Can anybody recommend other spices that go well in butter?
Garlic and parsley, specifically for melting on top of animal proteins.
^ that.
Also, dill or parsley.
Chives, specifically fresh chives. I have a bunch in my yard, but store-bought fresh chives would work too.
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You can make compound butter with pretty much any herb you wish as long as you use it with the appropriate dish. We’ve made them with tarragon, parsley, dill, and rosemary. Add lemon and/or garlic as desired.
And while not a herb or spice, anchovy butter is heavenly on vegetables, fish or beef.
Beurre de maitre d’hotelfor the win. Goes on anything.
Otherwise, lightly sauteed minced shallots make a nice spread with butter.
Cream butter and a smidgen of bleu cheese and chives/shallots for a nice steak topping.
If you want to jump down the rabbit hole a little further, try making a bearnaisesauce. Not much more complicated than a compound butter. I’ve been perfecting my old-school Frenchy sauces this year, and it’s loads of fun. For example, I made a Bearnaise with a dash of Angostura and some orange zest to go over St. Paddy’s corned beef and cabbage, and we were licking the sauce boat clean.
Oh, and I’ve made flavored butter with dried porcini and onion powder which was tasty over baked potatoes and pork chops.
I maintain my assertion that brandy is a herb.
For garlic butter, do you recommend minced or diced?
You want it finer than a mince, almost like a puree with no discernible flesh. Grate it with an oroshigane to get the right consistency.
my absolute favorite! 
I use thyme and rosemary butter, sometimes with sage, on everything I make in the fall right through Christmas. Excellent on breads, winter squash, turkey, potatoes, and, well, everything. I usually make about 3 pounds and find the last bit in the back of the freezer the next summer.
Have you tried adding honey and/or maple, and/or cinnamon? It makes a great breakfast butter.
Ginger raisin. I had it about 15 years ago at Mangoes down in Orange Beach. It was warm from the ginger and ever so slightly sweet from the raisins. I thought there would be hunks of raisins in it, but there weren’t. It was very smooth and yummy.
Cilantro-lime-garlic! On a grilled skirt steak.
Chives and parsley–not at the same time. Dried tends to keep better if I’m not using it all right away.
Tarlek
We made some cumin-cilantro-cayenne butter to use on hot cornbread and it was pretty delectable.
Tarragon pleases me a great deal, so tarragon.
I make porcini butter from time to time. Whiz up some dried porcinis into a powder, mix em into soft butter, let stand for some time to let the fat-soluble flavanoids settle in, then top steak, stuff under chix skin… I’ll bet dried morels work really well too.
I just discovered this, too. The one I had was from some grain-free recipe book or site and was used to add flavor to filet mignon. I don’t even remember what herbs were in it- probably the standard ones mentioned to “melt on animal protein.” I still have a log of it and have been putting it on everything.