Add the oil, milk, water, flour, salt, and vanilla. Mix just to combine.
Refrigerate the crepe batter for at least 30 minutes before using.
Grease a nonstick skillet and heat over medium-high heat. Once the skillet is heated raise it up above the burner and pour the crepe batter into the skillet using a ladle. Make sure the skillet is tilted at an angle as you pour the batter in. Begin swirling the skillet until all of the batter is spread evenly throughout the bottom. You want to have a pretty thin layer. Once the edges of the crepe begin to lift, run a rubber spatula around the sides then flip it over. Cook it for a few more seconds and flip it over onto a dish.
To assemble the crepe: add about 2-3 tablespoons of blueberry filling in the center of the crepe. Spread it into a long strip, leaving about 1 1/2 inches of space from the top and button. Then add a strip of whipped cream right over the blueberry filling. Fold the top and bottom of the crepe over. Then fold the sides. One side will be tucked before folding. This will make the crepe look more clean and pretty.