Mix flour, salt, and sugar in a medium bowl, and make a well in the center. Put egg, milk, olive oil, and vanilla in the well. Using a wooden spoon, gradually combine the dry and wet ingredients. Pour mixture into a blender, and liquefy. Let batter rest at room temperature for 30 minutes. Heat a nonstick crepe pan over medium-high heat. Spray pan with olive oil. Ladle 1/3 cup batter onto the center of the pan, lift the pan from the heat, and quickly swirl the batter to evenly coat the pan. Return to heat, and when small bubbles begin to form and the edges begin to brown and lift slightly, flip the crepe over using a wood blade or heatproof rubber spatula. After 1 minute, remove the crepe, setting it face down on a plate. Repeat, stacking finished crepes and separating them with wax paper. Set aside to cool. Makes approximately 10 crepes; can be made ahead.
Whip cream with sugar until soft peaks form. Set aside a small portion of the cream.
Using a small wire whisk or bamboo tea-whisk, beat matcha into 2 tablespoons boiling water until if forms a thick, syruplike consistency. Add tea solution to whipped cream, and blend gently. The cream should not be very sweet, but you can add more sugar to taste.
Re-stack crepes, discarding wax paper and placing the most attractive one on top. Carefully cut the stack into six wedges. Fill each wedge of mille-feuille by spreading small amounts of green-tea cream layer by layer. Place a dollop of the reserved whipped cream on each piece. If you like, you can garnish with fig wedges and a sprig of mint for an artistic presentation.