Two cups almond milk may be used in place of soy milk.
Combine milk, flour, oil, sugar, baking powder, and salt in a blender; process until smooth and combined. Refrigerate until cool and thickened slightly, at least 30 minutes and up to 1 day.
Heat a 10-inch nonstick skillet (pan should measure 8-inches across the bottom) over medium, and brush with oil. Pour a scant 1/4 cup batter into pan, turning and tilting skillet to coat bottom evenly. Cook until top of crepe appears set, bottom is firm and golden brown in spots, and edges lift from pan, 1 to 2 minutes. (If batter is too thick and does not spread evenly to edges of pan, whisk in more milk, 1 tablespoon at a time, to reach desired consistency.)
Slip a spatula under crepe, and gently flip in one swift gesture. (Use the spatula to unfold or rearrange crepe, as needed.) Cook until bottom is firm and golden brown in spots and edges are crisp, 30 to 45 seconds. Transfer to a plate, and cover. Repeat with remaining batter, brushing pan lightly with oil every 2 or 3 crepes, or as needed. Stack crepes and keep covered to keep them tender and pliable.