How to Make It
Fill a large pot with water, season well with salt, and bring to a boil.
Cook ham in a large deep nonstick frying pan over medium-high heat until lightly browned. Transfer to a small bowl and cover to keep warm. Don't wash pan.
In a large deep bowl, whisk together eggs and large pinch each of salt and pepper.
Add butter to pan. Using a Microplane, grate ginger into pan. Melt butter over medium heat, then cook until ginger is fragrant but before butter begins to brown. Remove from heat.
Boil udon until cooked through but slightly chewy, 2 to 3 minutes. Reserve 1/2 cup pasta water. Drain noodles, then immediately mix into ginger butter.
Whisk 1 tbsp. pasta water into egg mixture. Pour hot noodles into egg mixture and toss to coat evenly. Return noodles to pan over low heat and cook, stirring, until noodles are well coated and glistening. Add reserved pasta water, 1 tbsp. at a time, until coating is creamy and loose. Divide among four bowls and top with ham and onions.
*Most grocery stores carry packaged udon in the refrigerated section near the produce.