1. Preheat oven to 325°. Sift together flour and 3/4 cup sugar. Sift again and set aside.
2. In a large bowl or standing mixer, beat egg whites until foamy. Add cream of tartar and salt. Beat until soft peaks form. Add 3/4 cup sugar and the vanilla and almond extracts. Continue beating until egg whites are firm but not dry.
3. Sift one-third of the flour-sugar mixture onto the egg whites and, with a rubber or silicone spatula, gently fold the mixture into the egg whites. Add remaining flour in two batches, folding gently after each addition. Turn batter into an ungreased 10-inch tube pan and bake until browned and firm to the touch, 50 to 60 minutes.
4. Invert cake (in pan) on a cooling rack for at least an hour. When completely cool, run a long, thin, sharp knife between cake and pan to loosen, and remove cake.
5. Put candy canes in a large sealable plastic bag. Crush them into small pieces with a meat pounder, rolling pin, or the bottom of a small frying pan. Sift crushed candy with a fine-mesh strainer and reserve candy dust for another use (see Notes). Set crushed candy aside.
6. In a large bowl, beat cream with remaining 1/4 cup granulated sugar until soft peaks form. Frost cake with whipped cream using a spatula to form swirls and peaks. Sprinkle frosted cake with crushed candy canes. (To get candy on the sides, hold your hand about 1 in. from the cake and gently toss crushed candy at the sides.) Serve immediately, using a serrated knife to cut slices.
Note: Nutritional analysis is per serving.
The very fine candy "dust" left over from crushing the candy canes is delicious sprinkled on vanilla ice cream or stirred into hot cocoa. Add the crushed candy just before serving; the moisture from the whipped cream makes the peppermint begin to "melt" after half an hour.