In a medium bowl, whisk together the flour, baking powder and 1/2 teaspoon kosher salt.
With the mixer on low speed, add one-third of the flour mixture to the butter mixture, mixing until just combined. Add half of the date purée and mix to incorporate. Repeat with another one-third flour, the remaining date purée, and then finish with the final one-third flour, scraping the bowl after each addition. Mix only enough to combine.
Evenly scrape the batter into the prepared ramekins (or muffin tins). Bake until the cakes are golden and a tester comes out with moist crumbs, about 30 minutes. Don't overbake; you want them to be slightly puddinglike, but the tester shouldn't be wet.
To prepare toffee sauce: While the cakes are baking, in a small saucepan over medium-high heat, combine the cream, 1 cup brown sugar, 2 tablespoons rum, 2 tablespoons unsalted butter and 1/2 teaspoon kosher salt, and bring to a boil, stirring constantly. Reduce heat to medium-low and simmer until thicker, about 5 minutes. Remove from heat.
When the cakes come out of the oven, using a skewer, poke holes every 1/2 inch, through to the bottoms, and spoon two-thirds of the sauce over the tops, dividing the sauce evenly between cakes. If the sauce doesn't get completely absorbed into the cake, poke a few more holes.
Let the cakes cool for 10 minutes, then invert onto individual plates and spoon the remaining sauce over the tops. Serve immediately with ice cream. If you don't use all the cakes at once, keep them in their ramekins (or muffin tins), tightly covered, and refrigerate for up to 24 hours. Microwave for several seconds before serving with remaining sauce.