Baked goods and cooked dishes made from the five grains (wheat, barley, spelt, oats and rye) get Borei Minei Mezonot.
After eating: The short three-in-one blessing, Al Hamichya, after eating a kezayit.
Bracha on bourekas
BeforeMezonot
AfterAl Hamichya
בָּרוּךְ אַתָּה ה׳ אֱלֹקֵינוּ מֶלֶךְ הָעוֹלָם, בּוֹרֵא מִינֵי מְזוֹנוֹת
Baruch atah Hashem, Elokeinu melech ha'olam, borei minei mezonot.
Blessed are You, Hashem our God, King of the universe, who creates various kinds of nourishment.
This follows the common ruling of most poskim. For different customs or a specific question, ask a rabbi.