Prep the pan and oven. Heat the oven to 350°F (175°C). Butter a 9-inch square pan or a similar 2-quart baking dish, then line the bottom with parchment for easy release.
Soften the dates. Chop 1 1/2 cups pitted dates. Put them in a heatproof bowl.
Pour 1 cup boiling water over the dates and stir in 1 teaspoon baking soda. Let sit 10 minutes to soften and cool slightly.
Blend or mash. Use an immersion blender to puree the date mixture until mostly smooth, or mash with a fork for a chunkier texture. Either works—pureed gives a finer crumb; chunky adds little caramel-like bites.
Cream the butter and sugars. In a mixing bowl, beat 1/2 cup unsalted butter (softened) with 1/2 cup dark brown sugar and 1/4 cup granulated sugar until light and fluffy, about 2 minutes.
Add molasses and eggs. Beat in 1/4 cup molasses until combined.
Add 2 large eggs, one at a time, mixing well after each. Stir in 1 teaspoon vanilla extract.
Mix dry ingredients. In a separate bowl, whisk 1 1/2 cups all-purpose flour, 1 1/2 teaspoons baking powder, 1 1/2 teaspoons ground ginger, 1 teaspoon cinnamon, 1/4 teaspoon nutmeg, 1/8 teaspoon cloves, and 1/2 teaspoon salt.
Combine batter. Add half the dry ingredients to the butter mixture and mix just until combined. Stir in the warm date puree.
Add the remaining dry ingredients and mix until no dry spots remain. Do not overmix.
Bake. Scrape the batter into the pan, smooth the top, and bake 28–35 minutes, or until the center springs back and a toothpick comes out with a few moist crumbs. While it bakes, make the sauce.
Make the toffee sauce. In a saucepan, melt 1/2 cup unsalted butter with 1 cup dark brown sugar over medium heat, stirring until the sugar dissolves and the mixture is glossy, 2–3 minutes.
Add 3/4 cup heavy cream and a pinch of salt. Simmer gently for 3–4 minutes, stirring, until slightly thickened. Remove from heat and stir in 1 teaspoon vanilla.
Soak the pudding. When the cake is done, poke holes all over with a skewer.
Pour about half the warm toffee sauce evenly over the hot cake. It will soak right in.
Rest and serve. Let the pudding sit 10–15 minutes to absorb the sauce. Serve warm with extra toffee sauce at the table.
Add a scoop of vanilla ice cream or a spoonful of whipped cream, if you like. A pinch of flaky sea salt on top is lovely.