Preheat oven to 400°F. Grease two ramekins with the additional coconut oil and dust the insides with the additional cocoa powder, tapping out any excess. Set the ramekins aside.
Place 3 oz dairy-free dark chocolate and 1 tablespoon coconut oil in a large microwave-safe bowl. Microwave at 50% power for 30 seconds, stir, then continue microwaving in 30-second bursts, stirring after each, until the chocolate is fully melted and smooth. Set aside to cool slightly.
While the chocolate is melting, combine 1 large egg, 1 egg yolk, 1/4 cup coconut sugar, 3 tablespoons unsweetened applesauce, 1/4 teaspoon vanilla extract, and a pinch of sea salt in a large bowl. Use an electric hand mixer to beat until the mixture lightens in color and the coconut sugar begins to break down, about 2 minutes.
Pour the beaten egg mixture into the melted chocolate and coconut oil, whisking constantly until fully combined and the mixture begins to thicken slightly. Gently fold in 2 tablespoons cocoa powder until evenly incorporated.
Divide the batter evenly between the two prepared ramekins, filling each just over halfway. Spoon 2 teaspoons organic strawberry fruit spread into the center of each ramekin. Divide any remaining batter equally over the fruit spread so each ramekin is just over 3/4 full; smooth the tops lightly.
Place the ramekins on a baking sheet and bake in the preheated oven until the outside is set but the center appears slightly soft and undercooked, about 10 minutes.
Remove the ramekins from the oven and let them stand for 1 minute. Run a small knife around the inside edge of each ramekin to loosen the cake. Place a plate on top of a ramekin, invert the plate and ramekin together, then lift the ramekin off so the cake releases onto the plate. If a cake sticks, wait an additional 30 seconds and try again.