Position rack in center of oven and heat to 350 degrees. Lightly coat 9-inch round cake pan with olive oil and line bottom with parchment paper. Lightly coat parchment with olive oil.
In large mixing bowl, combine flour, sugar, cocoa, baking powder, baking soda and salt. Stir in half-and-half, 1/2 cup olive oil and vanilla.
With electric mixer, beat in egg until well blended. Scrape batter into prepared cake pan and sprinkle top with 1/4 cup mini chips.
Bake cake for 25-30 minutes, or until toothpick inserted into center comes out clean. Place cake on cooling rack 10 minutes, then turn cake out onto rack and let cool completely.
In medium saucepan, heat dulce de leche over medium heat, stirring occasionally, until softened. Add remaining olive oil and chocolate chips and stir until chocolate has melted and mixture is smooth. Remove pan from heat.
Transfer cake to serving plate. Pour icing over cooled cake, sprinkle with flaky salt, if desired, and serve.