Preheat the oven to 375° F. Butter or spray a 9x5" loaf tin, and line the width with a strip of parchment, overhanging the long sides by a few inches on each side for easy removal later.
In a large bowl, beat the butter and brown sugar until light and fluffy. Beat in the eggs one at a time, scraping down the sides of the bowl. In a small dish, stir together the vanilla, instant espresso and salt; add to the butter mixture and mix to combine.
Stir in the melted, slightly cooled chocolate, then add the flour and baking soda, stirring just to combine. Add the boiling water slowly and carefully, beating on low or stirring by hand to prevent sloshing. It will have the consistency of buttermilk - far thinner than a regular cake batter. Pour into the lined tin, place on a rimmed baking sheet and bake for 30 minutes, then turn the oven down to 325° F and continue to cook for another 15-25 minutes. You can tell it's done when the middle of the top is matte; no longer shiny, loose and wobbly. As Molly puts it, a knife in the center will not return the standard dry crumb, but neither do you want a long streak of batter - very damp crumbs are ideal.
Let the cake cool in its pan on a wire rack - it will sink in the middle, and it's supposed to. Lift it out using the parchment "handles" and serve in slices.