Cream the butter and sugar until light and fluffy, 3 to 4 minutes. Add the egg whites slowly, scraping down the bowl between additions. Add the flour on low speed until just incorporated.
Spread 20g / .71oz of the batter into a 10cm / 4in circular stencil on a nonstick rubber mat with a small offset spatula. Repeat until the nonstick rubber mat is filled with circles (about 12 circles per mat), leaving 2.5cm / 1in between each circle.
Bake until golden brown, about 6 minutes, and shape around a metallic cornet mold 10cm / 4in long by 3.75cm / 1.5in diameter while hot. If the cones cool off and become too firm to shape around the tube, return the sheet pan with the cones to the oven to soften them. Repeat with the remaining batter.
Reserve the finished cones in an airtight container at room temperature. Discard after 2 days.