Special equipment: Two to four 3 1/2-inch pastry rings 3 1/2-inch round cookie cutter
Heat the milk and water gently in a small saucepan until just warm but not hot. Place the potato flour, all-purpose flour and yeast in a bowl and mix well. Pour the warm milk and water over the dry ingredients and whisk until smooth. The batter should be the consistency of half-and-half; if it is too thick, whisk in 1 to 2 tablespoons more water. Cover the bowl with plastic wrap and leave to rest at room temperature for 1 hour to 2 hours, until lots of bubbles have formed on the surface.
In the meantime, preheat the oven to 390 degrees F for a convection oven or 450 degrees F for a regular oven. Place the tomatoes (keep them on the vine) on a baking sheet lined with parchment paper and sprinkle with kosher salt. Roast until the tomatoes just burst, about 10 minutes. Set aside.
Turn the oven down to 320 degrees F for a convection oven or 375 degrees F for a regular oven. Whisk the baking powder and fine salt into the batter.
Heat a heavy nonstick skillet over medium-high heat. Add 2 tablespoons oil. Place greased 3 1/2-inch pastry rings into the skillet (you should be able to fit 2 to 4 in the skillet). Pour 1/3 cup of the batter into each ring. Cover the skillet and reduce the heat to medium-low. When the surface of the crumpets is just set and bubbles form, about 5 minutes, remove the rings and flip the crumpets over with a spatula. Cook the other sides until they are golden, 2 to 3 minutes. Transfer crumpets to a wire rack. Repeat with the remaining batter. This should make 4 to 5 crumpets. (Sometimes the first one is a dud).
Add 1 tablespoon of the oil to another large skillet and place over medium-high heat. When hot, add the ham steaks and cook 2 to 3 minutes. Flip the steaks and cook the other side 1 more minute. Spread the tops of the steaks with the mustard and then the maple syrup. Slide the steaks out of the pan onto a baking sheet. With a 3 1/2-inch cookie cutter, cut our 4 circles from the steaks. Place them in the oven to keep warm while you make the eggs.
Grease the pastry rings once again. Heat the remaining 1 tablespoon oil in a large skillet over medium heat. Place the rings in the skillet and crack an egg into each. Fry the eggs inside the rings until the whites have set, 2 to 3 minutes.
To serve, place the crumpets on plates and top each with a piece of ham and a fried egg and drape tomatoes over the top.
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