Beat eggs until frothy. Combine dry ingredients; add to eggs alternately with milk, beginning and ending with flour mixture. Beat until smooth; stir in vanilla. Chill 1 hour. (This allows flour particles to swell and soften so crêpes are light in texture.)
Brush the bottom of a 6-inch crêpe pan or heavy skillet with oil; place over medium heat just until hot, not smoking.
Pour 2 tablespoons batter into pan; quickly tilt pan in all directions so batter covers bottom of pan. Cook crêpe 1 minute.
Lift edge of crêpe to test for doneness. Crêpe is ready for flipping when it can be shaken loose from pan. Flip crêpe, and cook 30 seconds. (This side is rarely more than spotty brown; fold this side to the inside.) Cool crêpe on a towel. Repeat procedure until all batter is used; stir batter occasionally. Stack crêpes between layers of waxed paper to prevent sticking.