Sift flour, 1 tablespoon sugar, baking powder, and salt together in a large bowl. Whisk milk, butter, eggs, and vanilla extract into flour mixture until smooth.
Heat vegetable oil in a skillet over medium-high heat. Scoop about 1/4 cup batter and pour onto hot skillet. Tilt the pan in a circular motion to evenly distribute the batter. Cook crepe until bottom is lightly browned, about 2 minutes. Loosen with a spatula, flip, and cook the other side, about 2 more minutes. Transfer to a plate. Add more oil to the pan and repeat with remaining batter.
Mix coconut, 1 tablespoon white sugar, and cardamom together in a small bowl. Spread 1 to 2 tablespoons of coconut mixture into the center of each crepe; fold crepe over the filling like an envelope or in half.