Responsa for Berakhot 83:7
אמר רב הרגיל בשמן שמן מעכבו אמר רב אשי כי הוינן בי רב כהנא אמר לן כגון אנן דרגילינן במשחא משחא מעכבא לן ולית הלכתא ככל הני שמעתתא אלא כי הא דאמר רבי חייא בר אשי אמר רב שלש תכיפות הן תכף לסמיכה שחיטה תכף לגאולה תפלה תכף לנטילת ידים ברכה
Rab said : He who is accustomed [to anoint his hands] with oil [after finishing a meal], the oil impedes him Rab Ashe said : When we were at the school of Rab Kahana, he said to us, "For instance we are accustomed to the use of oil, and the oil impedes us." But the Halakah is in agreement with none of these teachings, but with that which Rab Hiyya b. Ashe said in the name of Rab, viz.: There are three actions which have to be performed with dispatch : the putting on of hands must be followed immediately by the act of slaughtering ; the Tefillah must follow immediately on the Ge'ullah ; and the Grace after meals must follow immediately on the washing of the hands.
Teshuvot Maharam
A. There exists a difference of opinion among the Geonim, but I believe that he should wash his hands once, and recite two blessings: the first "on the washing of hands" and the second "who has created Man", and then eat.
SOURCES: Pr. 42; L. 347; Hag. Maim., Berakot 6, 50.