mid-14c., crustade, "meat or fruit pie, any dish baked in a crust" from Anglo-French croustade (Modern French coutarde), from Old Provençal croustado "fruit tart," literally "something covered with crust," from crosta "crust," from Latin crusta "rind, crust, shell, bark" (from PIE root *kreus- "to begin to freeze, form a crust").
In Middle English also crustard, custade, etc. Meaning shifted c. 1600 to "compound of eggs and milk, sweetened and baked or boiled." The spelling change (by mid-15c.) is perhaps by influence of mustard. OED notes that custard-pie (by 1825) was "commonly used as a missile in broad comedy."
c. 1300 (probably older; piehus "bakery" is attested from late 12c.), "baked dish of pastry filled with a preparation of meats, spices, etc., covered with a thick layer of pastry and baked," from Medieval Latin pie "meat or fish enclosed in pastry" (c. 1300), which is perhaps related to Medieval Latin pia "pie, pastry," also possibly connected with pica "magpie" (see pie (n.2)) on notion of the bird's habit of collecting miscellaneous objects.
According to the OED, the word is not known outside English with the exception of Gaelic pighe, which is from English. In the Middle Ages, a pie had many ingredients, a pastry but one. Fruit pies began to appear c. 1600.
The word in the figurative sense of "something easy" is from 1889. Slice of the pie in the figurative sense of "something to be shared out" is by 1967. Pie-eyed "drunk" is from 1904. Phrase pie in the sky is attested by 1911, from Joe Hill's Wobbly parody of hymns. Pieman "baker or seller of pies" is by c. 1300 as a surname. Pie chart is from 1922.
"magpie," mid-13c. (late 12c. as a surname), from Old French pie (13c.), from Latin pica "magpie" (see magpie).
to eat humble pie (1830) is from umble pie (1640s), pie made from umbles "edible inner parts of an animal" (especially deer), considered a low-class food. The similar sense of similar-sounding words (the "h" of humble (adj.) was not then pronounced) converged to make the pun. Umbles is Middle English numbles "offal," with loss of n- through assimilation into preceding article.
"open tart," 1846, from French flan "custard tart, cheesecake," from Old French flaon "flat-cake, tart, flan" (12c.), from Medieval Latin flado (10c.), which probably is from Frankish *flado or another Germanic source (compare Old High German flado "offering cake," Middle High German vlade "a broad, thin cake," Dutch vla "baked custard"), from Proto-Germanic *flatho(n) "flat cake," which is probably from PIE root *plat- "to spread." Borrowed earlier as flawn (c. 1300), from Old French.