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Preheat oven to 350 degrees F. Butter either a 9-inch springform pan or 2 6-inch cake pans. (If using a non-springform pan, line the bottom of the pan with parchment paper buttered on both sides.)
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In a small saucepan, bring dates and water to a simmer over medium heat. Cook until dates start to soften, about 1 minute. Remove from heat and immediately stir in baking soda. Set aside to cool.
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In a medium bowl, whisk together flour, baking powder, and salt. In a large bowl, use an electric mixer to beat butter and sugar on medium speed until pale and fluffy 3 - 4 minutes. Beat in eggs, one at a time, and then add ginger. Add flour mixture and beat until just combined. Stir in date mixture and fold in apples. Spoon batter into prepared pan and smooth the top. Bake until a toothpick inserted in the center comes out with a few moist crumbs attached, 40 - 45 minutes.
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Meanwhile, prepare the sauce by combining the brown sugar, butter, and salt in a medium saucepan set over medium heat. Cook, stirring occasionally, until butter has melted and the sugar's dissolved – about 3 minutes. Stir in cream, bring mixture to a gentle simmer, and then turn heat to low. Cook, stirring constantly, until sauce has thickened, 5 - 7 minutes. Set sauce aside to cool slightly.
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Cool cake for 15 minutes, then remove sides (or flip out of cake pan) and set on a serving plate. Use a toothpick to poke holes all over cake. Pour half the warm sauce over the cake. Slice, and serve warm cake with a generous drizzle of sauce.
Leftovers will store well wrapped at room temperature for 3 days.