Bring a large pot of a water to a boil and then add the cauliflower florets. Boil until the stem parts are tender (about 10 minutes). Drain and let the cauliflower cool enough to handle. Mince and the cauliflower so that it forms a rough meal with each piece about the size of a large grain of rice.
Add the cauliflower, ground pork, garlic chives, gorgonzola, soy sauce, potato starch, toasted sesame oil, and black pepper to a bowl. Put some gloves on and use your hands to knead the mixture together until smooth, breaking up the gorgonzola as you go. You want to leave some small lumps of gorgonzola, but there should not be any large chunks.
Wrap the gyoza. Check out this post for an animated gif, or this post for set by step photos.
Add 1 tablespoon of vegetable oil to a non-stick frying pan and swirl to coat evenly. Add the pot stickers to the pan either placing them in rows, or in a circle (as shown). The potstickers should be touching each other, but be careful not to overcrowd the pan. How many potstickers you'll be able to fry at one time will depend on the size of the pan, but don't use a pan that's much larger than the heating element of your stove otherwise the gyoza won't brown evenly.
Prepare 1/4 cup of water with 1/2 teaspoon of potato starch mixed in.
Turn the heat onto medium-high heat and fry the gyoza until they just barely start to brown on the bottom.
With a lid in one hand to shield yourself from any splattering oil, add the water and potato starch mixture around the gyoza and immediately cover the pan with the lid. Steam for 3 minutes, or until the water is almost all gone (if the water evaporates before 3 minutes, open the lid a crack and add a bit more).
Remove the lid and fry until golden brown on the bottom. Invert onto a plate and serve with the dipping sauce. Repeat with the rest of the potstickers.