Make the cake:

Step 1: Make the cake:

Place 6 tablespoons unsalted butter in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Place 2 large eggs on the counter. Let both sit at room temperature until the butter is softened.

Step 2: Make the cake:

Arrange a rack in the middle of the oven and heat the oven to 350˚F. Coat a 9x9-inch square baking dish with butter.

Step 3: Make the cake:

Place 8 ounces pitted dates and 1 teaspoon baking soda in a medium bowl. Pour 1 cup boiling water over the dates and let stand until softened, about 10 minutes. Scrape the date mixture into a food processor fitted with the blade attachment and process until puréed, 20 to 25 seconds.

Step 4: Make the cake:

Wipe the bowl the dates were in dry. Place 1 1/2 cups all-purpose flour, 1 1/2 teaspoons baking powder, 1/2 teaspoon kosher salt, 1/2 teaspoon ground cinnamon, 1/4 teaspoon ground cloves, and 1/8 teaspoon ground nutmeg in the bowl. Whisk until combined.

Step 5: Make the cake:

Add 3/4 cup packed dark brown sugar to the bowl of butter. Beat with the paddle attachment on medium speed until combined, about 1 minute. Add 1 of the eggs and beat on medium speed until combined, then add the second egg and beat until just combined. Add the date purée and 1 1/2 teaspoons vanilla extract and beat on medium speed until just combined. Scrape down the sides of the mixer.

Step 6: Make the cake:

Add the flour mixture to the date mixture and beat on the lowest speed until just combined, scraping down the sides of the bowl as needed. Transfer the batter to the baking dish and smooth into an even layer.

Step 7: Make the cake:

Bake until the cake is set and a tester inserted into the center comes out clean, 30 to 35 minutes. Immediately use the tines of a fork to poke holes all over the cake, poking all the way down to the bottom and spacing the pokes about 1/2-inch apart.

Make the sauce:

Step 1: Make the sauce:

Melt 1 stick unsalted butter in a medium saucepan over medium-high heat. Add 1 1/4 cups packed dark brown sugar, 1 cup heavy cream, 2 teaspoons vanilla extract, and 1/2 teaspoon kosher salt. Stir until smooth and glossy, about 1 minute.

Step 2: Make the sauce:

Remove the saucepan from the heat. Drizzle 1 cup of the sauce over the warm cake. Return the pan to the oven and bake until the sauce bubbles, about 5 minutes. Sprinkle with flaky salt if desired. Serve the toffee pudding hot with the remaining sauce and vanilla ice cream.