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Preheat the oven to 375°F. Using a pastry brush, generously butter the bottoms and sides of each ramekin. Sprinkle the buttered ramekins with sugar, shake to fully coat the sides, then tap out any remaining loose sugar and discard. Place the prepared ramekins on a baking sheet.
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In a large, heat-proof bowl, whisk the egg yolks, 3 tablespoons (37g) of the sugar, salt, and espresso powder until thickened, about 1 minute.
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Add the milk and cocoa powder, whisking until combined.
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Place the bowl over a saucepan that has about 1" to 2" of simmering water in it (you should just barely see some bubbles across the surface of the water). Whisk gently and continuously until the cocoa powder is fully hydrated and the mixture is smooth, 2 to 3 minutes.
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Remove the bowl from the heat and add the chocolate and vanilla. Let the mixture rest for a few minutes, then whisk until smooth. The chocolate should be completely melted, and the mixture will be thick and glossy. Set aside while you whip the egg whites.
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In the bowl of a stand mixer fitted with the whisk attachment or working in a large mixing bowl with an electric hand mixer, whip the egg whites and cream of tartar until soft peaks form. With the mixer running, gradually add the remaining 3 tablespoons (37g) sugar and continue to whip until the mixture is light and billowy and medium peaks form.
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Using a whisk, fold 1/3 of the beaten egg whites at a time into the chocolate mixture until no white streaks remain. A whisk, rather than a spatula, will incorporate the egg whites more evenly and in fewer strokes.
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Portion the chocolate soufflé batter evenly into the prepared ramekins, filling them to the very top. A scone and muffin scoop is helpful here; start with 2 rounded scoops per ramekin and then divide any remaining batter evenly.
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Bake the chocolate soufflés for 18 to 22 minutes for 4-ounce soufflés or 20 to 25 minutes for 6-ounce soufflés, or until they've risen and the tops feel firm to the touch. If your oven is known to have hot spots, gently rotate the pan after 10 to 12 minutes to ensure even heat distribution. (The cream of tartar in the egg whites helps stabilize the soufflés and reduces the likelihood that they'll collapse when the oven door is opened, so don't be afraid to rotate the pan halfway through, if needed.)
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Remove the chocolate soufflés from the oven, dust with Snow White Non-Melting Sugar or confectioners’ sugar, and serve immediately.
