For apricot filling, drain the juice from 2 cans apricots and place in a small saucepan. Set apricot halves aside. Bring drained syrup to boiling, remove from heat. Add dried apricots. Let stand 15 minutes to soften. Drain and discard liquid.
In a food processor or blender combine the dried apricot halves and the softened dried apricots. Cover and process or blend until smooth. Transfer to a bowl. Stir in the honey and lime peel; set aside.
In a large bowl whisk together eggs, buttermilk, and melted butter until combined. Add flour, almond flour, sugar, baking powder, baking soda, and salt. Whisk until smooth.
Pour about 1/2 cup batter onto a hot, lightly greased griddle or heavy skillet. Spread batter to a 7-1/2- to 8-inch circle. Cook over medium heat for 1 to 2 minutes, turning cake when surface is bubbly and edges are slightly dry. Cook cake 1 minute more until golden brown.
Place cake in an 8-inch springform pan. Top with 1/3 to 1/2 cup of apricot filling. Repeat with remaining batter and filling, finishing with apricot filling on top. Yields 6 or 7 layers. Cover and chill 2 hours or overnight.
To serve, top with whipped cream, sprinkle with lime peel, and drizzle with honey. Top with apricots, if desired.