Place the all-purpose flour, bread flour, cream of tartar, and salt in the bowl of a standing mixer fitted with the paddle attachment. Stir to combine.
Whisk together the water, yeast, and sugar in a medium bowl and let stand until foamy, about 10 minutes.
Pour the water mixture into the flour mixture and mix on low speed to combine. Cover the bowl with plastic wrap and let stand at room temperature for 1 to 1-1⁄2 hours.
Dissolve the baking soda in the milk, and then pour the milk mixture into the bowl with the batter. Stir gently to combine. The batter should now be the consistency of pancake batter. If it’s too stiff, your crumpets won’t have enough of those characteristic bubbles and holes, so, if necessary, add more water, a tablespoon at a time, to reach the right consistency.
Heat a large nonstick skillet over medium-low heat. Grease several 4-inch cake rings with butter.
Place the cake rings in the skillet and pour some batter into each ring so they’re three-quarters full. Cook until holes begin to form on the surface, 7 to 8 minutes. Remove the rings, flip the crumpets, and cook for another 2 to 3 minutes, until nicely toasted. Serve immediately with butter. For longer storage, freeze in a zipper-lock plastic bag for up to 1 month. To defrost, place on the countertop for 15 to 30 minutes, and reheat in the oven at 350°F for 5 minutes before serving.