Step 1 Heat the oven to 325 degrees.
Step 2 Cook the juice from the peaches in a heavy pot over medium heat until thickened to heavy syrup, 10 to 12 minutes. Pour the syrup into the bottom of an 11x7-inch baking pan. Add the 1/4 cup honey. Dot with the butter and arrange a thick layer of peaches over the top.
Step 3Beat the eggs yolks until thick and lemon-colored, 4 to 6 minutes. Gradually add the 2/3 cup honey, beating constantly. Add the lemon juice and blend. Add the hot water and beat hard for 3 minutes.
Step 4Sift together the flour, baking powder and salt and stir into the egg mixture.
Step 5Beat the egg whites until stiff, 3 minutes, and fold into the mixture. Pour the batter over the peaches and smooth with an offset spatula. Bake the cake until it's firm on top and golden brown and a toothpick inserted in the middle comes out clean, 30 to 35 minutes. Cut it into pieces and serve with whipped cream.