Preheat the oven and prepare the pan. Preheat the oven to 350°F (177ºC). Grease a 9-inch square baking pan and line the bottom with parchment paper. Lightly grease the parchment as well.
Mix the dry ingredients. In a medium bowl, whisk together the flour (2 cups), baking soda (1 1/2 teaspoons), salt (3/4 teaspoon), ginger (2 teaspoons), cinnamon (1 1/2 teaspoons), allspice (1/4 teaspoon), and cloves (1/4 teaspoon), until well combined. Set aside.
Cream the butter and sugar. In a large mixing bowl, beat the softened butter (1/2 cup) and dark brown sugar (1/2 cup) together with an electric mixer until creamy and slightly fluffy, 2–3 minutes.
Add molasses, egg, and vanilla. Beat in the molasses (3/4 cup) until fully combined. Add the egg (1) and vanilla (1 1/2 teaspoons) and mix just until smooth, scraping down the bowl as needed.
Combine the batter. With the mixer on low, add the dry ingredients in 2–3 additions, alternating with the boiling water (1 cup), beginning and ending with the dry ingredients. Mix just until the batter is smooth; it will be fairly thin.
Bake the cake. Pour the batter into the prepared pan and smooth the top. Bake for 30–35 minutes, or until the center springs back lightly to the touch and a toothpick inserted in the center comes out with a few moist crumbs, not wet batter.
Cool slightly. Place the pan on a wire rack and let the cake cool for at least 20 minutes before cutting. Serve warm or at room temperature.
Make the warm caramel sauce. While the cake cools, add the butter (1/2 cup), dark brown sugar (1 cup), heavy cream (1 cup), molasses (2 tablespoons), and salt (1/2 teaspoon) to a medium saucepan. Cook over medium heat, stirring frequently, until the mixture comes to a gentle boil. Simmer for 3–4 minutes until smooth and slightly thickened.
Finish the sauce. Remove the pan from the heat and stir in the vanilla (2 teaspoons). The sauce will thicken a bit as it cools. If it becomes too thick, thin with a splash of warm cream.
Serve. Cut the gingerbread cake into squares. Serve each slice warm with a generous spoonful of warm caramel sauce over the top.