Step 1In a heavy saucepan, heat the olive oil over medium heat. Add the shallots and sweat until softened, 5 to 7 minutes.
Step 2Stir in the bay leaf, salt and heavy cream. Bring to a gentle simmer and reduce the cream by one-third, 30 to 40 minutes. Remove the bay leaf, but do not strain the shallots. This makes 2 cups kuku cream.
Step 1Heat the oven to 350 degrees. Grease a 13- by 9-inch baking pan, and line the bottom with parchment paper. Grease the parchment paper.
Step 2Heat a large skillet over medium-high heat until hot. Add the olive oil. Saute the spinach (this may need to be done in batches; add additional oil if needed) until wilted, then remove from heat. Wring the spinach out using a large kitchen towel, squeezing out as much liquid as possible. Finely chop the spinach.
Step 3Combine the spinach, beans and kuku cream in a heavy saucepan and heat, stirring frequently, until the mixture is just above room temperature. Remove from heat.
Step 4Whisk the eggs until smooth, then pass through a strainer into a bowl, discarding any unstrained bits. Stir in the warmed cream mixture, along with the barberries and salt, to fully combine.
Step 5Pour the kuku mixture into the prepared pan. Bake until the egg is set and a knife inserted in the center comes out clean, 30 to 45 minutes, depending on the thickness of the kuku.
Step 6Cool before slicing.