Whisk all-purpose flour, cake flour, yeast, baking powder, and salt together in 8-cup liquid measuring cup. Add 1¼ cups warm water and whisk until smooth. Cover and let rise in warm place until doubled in volume, about 40 minutes.

Heat oil in 8-inch nonstick skillet over low heat for at least 5 minutes. While skillet heats, add remaining ¼ cup warm water to batter and whisk until smooth.

Increase heat to medium and heat skillet for 1 minute. Using paper towel, wipe out skillet, leaving thin film of oil on bottom and sides. Pour one-third of batter into skillet and increase heat to high. Cook for 45 seconds (bubbles will be visible just under surface of entire crumpet). Reduce heat to medium-low and continue to cook until edges are risen, set, and beginning to dry out, about 4 minutes longer. (Gently lift edge and peek at underside of crumpet occasionally; reduce heat if underside is getting too dark, and increase heat if underside doesn't appear to be browning.)

Slide skillet off heat. Place dry, flat spatula on top of crumpet and pull up sharply to remove excess batter and reveal holes. Scrape excess batter from spatula back into measuring cup. Repeat procedure until holes are exposed over entire surface. Flip crumpet, return skillet to burner, increase heat to high, and cook until edges of second side are lightly browned, 1 to 2 minutes. Invert crumpet onto wire rack. Immediately add half of remaining batter to skillet. Return skillet to high heat and repeat cooking process (omitting 5-minute preheat). Repeat with remaining batter. Let crumpets cool completely.

To serve, cut each crumpet into 4 wedges and toast until crumpets are heated through and exteriors are crisp. Spread crumpets generously with butter and jam or honey and serve. (Untoasted crumpets can be transferred to zipper-lock bag and refrigerated for up to 1 week or frozen for up to 1 month.)