Preheat oven to 350°F. Line a 9- x 5-inch loaf pan with parchment paper, leaving a 2-inch overhang on long sides. Spray parchment lightly with cooking spray; set aside.

Whisk together coffee, cocoa, and butter in a medium bowl until smooth and well combined; let stand 5 minutes. Add brown sugar, oil, and 2 teaspoons fine sea salt to coffee mixture; whisk until sugar dissolves and mixture is smooth, about 1 minute. Add eggs and 1/2 cup crème fraîche; whisk until batter thickens slightly, about 30 seconds. Add all-purpose flour, rye flour, and baking soda; whisk until all dry ingredients are just incorporated. Transfer batter to prepared pan.

Bake in preheated oven until cake forms a crust, cracks in the center, and springs back lightly when pressed, 1 hour to 1 hour and 20 minutes. Transfer pan to a wire rack, and let cake cool in pan 15 minutes. Run an offset spatula around edges of cake; using parchment overhang as handles, remove cake from pan. Transfer cake to wire rack, and let cool completely, about 2 hours. Remove and discard parchment paper.

Cook chocolate, corn syrup, remaining 1/2 cup crème fraîche, and remaining 1/4 teaspoon fine sea salt in a saucepan over low, whisking constantly, until chocolate is melted and mixture is smooth, about 2 minutes. Remove from heat; let cool until thickened and spreadable, 15 to 20 minutes, whisking every 5 minutes.

Spread chocolate mixture on top of cooled cake, letting some drip down cake sides. Let stand 5 minutes. Garnish with flaky sea salt and cacao nibs