Place a rack in the center of the oven and preheat to 325º. Have four 4 ounce ramekins ready, and an 8" square pan with 2" high sides.
Combine the caps, milk, cream and half the sugar in a small saucepan. Place over medium heat until bubbles form along the sides of the pan and the mixture steams, stirring occasionally. Remove from the heat, cover and steep for 30 minutes.
Meanwhile, make the caramel. Pour the water into the pot, then add the sugar, being careful not to get any crystals on the side of the pot. Add the cream of tarter, then bring to a boil over medium-high heat. Cook, without stirring, until the sugar dissolves, the mixture comes to a boil and the sugar begins to color. Gently tilt the pan to brown the sugar evenly. If any crystals cling to the sides of the pan, brush them down with a clean, wet pastry brush. When the sugar reaches a medium amber color, remove it from the heat and immediately pour into the bottoms of four 4 ounce ramekins, tilting to coat them with the caramel. (If you're wondering how the heck to get that residual hardened caramel out of the pot, pour some super hot water into it and let it sit for 10 minutes or so.) Place the coated ramekins in an 8" square pan with at least 2" high sides and set aside.
Back to the custard. Whisk the egg, yolks, salt and the other half of the sugar in a medium bowl to combine. Place the bowl on a damp towel. Re-scald the dairy, then slowly drizzle it into the egg mixture, whisking like mad. Strain the whole deal through a fine mesh sieve into a large pitcher, pressing the mushrooms to extract as much liquid as possible. (The shrooms can be rinsed and dried for another use, like making candy cap extract.)
Pour the custard into the caramel-lined rams, filling them evenly. Pour hot tap water into the pan, coming two-thirds of the way up the sides of the rams (this is easier if you remove one ram first). Cover with a sheet pan or aluminum foil (punctured a few times to keep the custards from over-steaming). Place in the oven. Bake for 45 minutes to an hour. The custards are ready when they have a uniform jiggle, like jell-o. They should not appear runny or liquid (underbaked), nor should they have bubbles along the sides (overbaked).
Remove the ramekins from the water bath when cool enough to handle. Chill in an ice bath if you like, and put them in the fridge when mostly cool for at least 12 hours, or up to a couple days.
To serve, dip the ramekin in a bowl of hot water for a few moments. Use the pads of your thumbs to gently press around the top of the custard, prying it away from the ramekin and breaking the seal. Upend over a plate or shallow bowl. Holding the ramekin and plate firmly between your thumbs and fingers, give it a firm couple of downward shakes. The custard and sauce should slurp out. (If this doesn't work, you can run a sharp knife around the sides of the custard.) Remove the ramekin and repeat with the remaining custards.