Make sandwich bread dough. Combine warm milk with honey and yeast, gently stirring to combine. Let sit for 10 minutes or until yeast is activated and mixture is foamy.
Combine yeast mixture with bread flour, egg, salt, and butter in the bowl of a stand mixer. Mix until a rough dough forms. Continue to knead dough until smooth, about 7-8 minutes. Transfer dough to a bowl, cover with plastic wrap, and let proof in a warm area for 1 hour or until doubled in size.
Punch down dough. Divide into 8 equal portions (about 78 grams each) and roll into balls. Loosely cover with a clean kitchen towel and let rest for 15 minutes.
Beat remaining egg in a large bowl and place panko in another bowl.
Working with one portion at a time, flatten the dough ball into a rectangle. Starting with the long side facing you, roll the dough into a log. Pinch close the seams and roll the log until it's 6 inches long.
Dip bread into beaten egg then coat in panko, making sure to cover all sides. Place on a baking sheet lined with parchment paper and loosely cover with a clean kitchen towel. Repeat with the remaining dough. Let proof for 45 minutes or until doubled in size.
Meanwhile, make lobster salad. Combine lobster with cooked corn, kewpie mayonnaise, lemon juice, and hot mustard. Season with salt and pepper. Set aside.
Heat frying oil to 325 degrees F.
Working in batches at a time, carefully drop the bread into the oil. Flip the bread over a few times while it's frying to get all sides evenly browned. You may need to hold it down to help even browning. Remove with a slotted spoon and place on paper towel-lined plates to drain excess oil. Repeat with remaining bread.
Cut a slit on the top of the bread rolls and fill with lobster salad. Top with chopped cucumber and serve immediately.