Stir together the chopped dates, boiling water, and baking soda in a heatproof bowl. Let sit for 20 minutes, until the dates are very soft. Reserve ¼ cup of the soaking liquid, then strain the dates through a fine-mesh sieve. Transfer the dates and reserved soaking liquid to a blender or food processor and blend until a thick, mostly smooth paste forms.

Preheat the oven to 350°F (180°C). Generously grease three 8-inch round cake pans and line the bottoms with greased parchment paper. Add the butter to a small saucepan and cook over medium-low heat until deeply golden with brown flecks. Set aside to cool until warm but not hot.

In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. In a large bowl, whisk together the slightly cooled browned butter and oil. Add the brown sugar and molasses and whisk until glossy and smooth. Add the eggs and whisk until smooth and emulsified. Whisk in the vanilla and sour cream until fully incorporated. Fold in the blended date mixture until evenly distributed.

Add the dry ingredients to the wet ingredients. Fold gently until just combined and no dry flour remains. Divide the batter evenly between the pans, smoothing the top with an offset spatula. Bake for 34-40 minutes, until the centers spring back lightly when pressed. Cool the cakes in their pans for 10 minutes, then turn out onto racks to cool completely.

Add the butter to a saucepan over medium heat. Once fully melted, add the brown sugar. Cook, whisking constantly, until the mixture is glossy and fully unified. Slowly whisk in the heavy cream. Reduce heat slightly and simmer for 3–5 minutes, until thickened and spoon-coating. Remove from heat and stir in the salt and vanilla. Cool completely until thick, smooth, and spreadable.

In the stand mixer fitted with the paddle attachment, beat the butter and cream cheese on medium-high speed until completely smooth. Add the powdered sugar and beat until creamy and aerated. Add the crème fraîche, vanilla paste or extract, and salt and beat until smooth.

Place the first cake layer on a serving plate or cake board. Spread a thin layer of frosting evenly over the top. Create a raised border of frosting around the edge, leaving a shallow well in the center. Spoon about ⅓ cup of toffee sauce over the frosting and spread into an even layer. Top with the second cake layer and repeat with frosting and toffee. Add the final cake layer and frost the outside of the cake with the remaining frosting. Dot small spoonfuls of toffee sauce around the sides and top.