Heat oven to 300 degrees. Cream butter and sugar in mixer on medium speed until fluffy. Mix in egg whites, one at a time. Fold flour into batter until well combined.
Place a nonstick baking mat on a baking sheet; place stencil in corner of mat. Spread a thin layer of batter over stencil with an offset spatula, then lift stencil away. Repeat to fill baking sheet. Bake until cookies are golden, 14 to 16 minutes. Use a small offset spatula to transfer cookies to a flat surface to cool. Store airtight up to 2 days.
To add gold flecks, lightly touch corner of gold leaf; a small piece will stick to your fingertip. Then gently transfer it to the tuiles.