Place a rack in the center of the oven and preheat to 350°F. Butter and flour the bottom and sides of a 9-by-13-in baking pan, spray with nonstick cooking spray, or butter and line the bottom of the pan with parchment paper.
In a medium bowl, whisk together the vegetable oil, honey, vanilla, and almond extract until well mixed. Whisk in the eggs and egg yolks until well combined. Whisk in the crème fraîche. In a separate medium bowl, stir together the all-purpose flour, almond flour, baking powder, baking soda, and salt. Using a rubber spatula, gently fold the dry ingredients into the wet ingredients until thoroughly combined. Scrape the batter into the prepared pan.
Bake for 30 to 40 minutes, or until the cake springs back when you poke it in the center and is pale golden brown. Remove from the oven and let cool completely in the pan on a wire rack.
Meanwhile, make the frosting: Using a stand mixer fitted with the paddle attachment (or with an electric hand mixer), beat the cream cheese on medium speed for at least 4 minutes, or until perfectly smooth. (Cream cheese has a tendency to lump up easily, so don’t skip this step.) Using a rubber spatula, scrape the bowl and add the butter. Add the honey, vanilla, almond extract, and salt and beat well on medium speed until thoroughly combined. The frosting can be stored in a covered container in the refrigerator for up to 1 week.
When the cake is completely cool, using a rubber spatula or an offset spatula, frost with creamy frosting and serve. The frosted cake can be stored, well wrapped with plastic wrap or in an airtight container in the refrigerator, for up to 3 days; remove at least 1 hour before serving so the cake is not cold.