Uta Hagen was my employer for more than ten years, but I've no anecdotes about her. I caught her on Broadway in a two-character play in which she had all the lines and Charles Nelson Reilly had none (!)
But my favorite Uta appearance is in Thomas Meehan's monologue, The Yma Dream, in which she gets introduced to Oona O'Neill, Ulu Grossbard and Yma Sumac in quick secession. ("Uta, Oona; Oona, Uta. Uta, Ulu; Ulu, Uta. Uta, Yma; Yma, Uta.")
On paper, Fiddler on the Roof may be the greatest musical ever. Glad BK liked my Supreme suggestion.