Maitre d'Hotel -- THE Compound ButterThe classic compound butter for grilled meats and fish is something called beurre maitre d'hotel aka maitre d'hotel butter in Franglaise. There are a lot of variations but the basic recipe is:
Beurre Maitre d'Hotel
8 oz unsalted butter,
Juice of 1 lemon
1 tbs chopped parsley
2 tsp chopped shallots
2 dashes Worcestershire sauce
Salt, to taste (about 1 tsp)
Pepper, to taste (about 1/2 tsp)
Soften, then cream the butter. Mix in the other ingredients, thoroughly. Taste and adjust for salt and pepper. Take the butter from the bowl and place on cling warp. Roll to from a log. Refrigerate for at least 6 hours before using to allow the flavors to marry.
Variations: Increase the lemon juice for fish. Add cheese to taste -- the most common are dry grated cheeses such as Parmiggiana, Romano, Cotijo, etc., or blue types. Instead of salt use chopped anchovies. Add chipotle hot sauce. Instead of shallots, use minced garlic -- in which case it becomes beurre escargot. Etc.
In the case of your wife's steak, the hint of sweetness probably came from the Worcestershire sauce.
I've never heard the term, "chef's butter" before. Any idea where you first heard it? Is it a common term in your region?
Hope this helps,