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1
Preheat oven to 350 F. Lightly grease insides and bottoms of two 8? cake pans, and line bottoms of pans with parchment; set aside. Finely zest the peel of one lemon; set zest aside. Juice the peeled lemon, plus 2-3 more, to make 3/4 cup lemon juice (seeds removed); set aside. Fill food processor with peas and peppermint leaves. Blend, gradually adding 1/2 cup of the lemon juice (reserve remaining 1/4 cup juice). Stop occasionally to scrape down sides, and keep blending for just a few minutes, until mixture is consistent and there are no remaining big leaf pieces or whole peas. Texture should be even but rather thick and not smooth. Set aside.
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2
With an electric mixer, beat egg whites on high speed, gradually adding 1/4 cup of the sugar once whites are foamy and becoming white. Keep beating until whites are fluffy, opaque, and hold quite solid peaks; set aside.
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3
In a large bowl, beat the remaining 3/4 cup sugar, oil and extracts until smooth. Gently fold in the pea mixture, stirring until even. Sift or sieve over the mixture: flour, salt, baking powder and soda. Mix until incorporated, adding remaining 1/4 cup lemon juice along the way. Fold in the vanilla bean seeds and lemon zest until just evenly disbursed. Gently fold in the egg whites 1/3 at a time until just incorporated, being careful not to flatten them too much. Batter will be frothy and delicate.
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4
Quickly transfer it equally into the prepared pans, spreading gently to edges. Bake for 25-35 minutes or until toothpick tests clean in center and edges are becoming golden brown. Cakes will be an unusual color and not very tall. Let them cool completely in pans before loosening edges with knife and removing. Once cool, cover until ready to frost or decorate, then store and serve at room temperature for up to 24 hours; do not refrigerate.
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5
Because the cake is best at room temperature, you'll want to wait to frost it until just ready to serve. This refreshing cake matches perfectly with a basic cream cheese icing, enhanced with some lemon juice and a drop of mint extract. To keep the dessert dairy-free, opt to frost it with meringue frosting such as 7 minute frosting. If desired, add a drop of green food coloring to your icing and/or decorate with peppermint leaves and even a few peas. Alternately, a simple dusting of sifted powdered sugar is divine.
