Japanese vegetable pancakes

Pancakes
1/2 small head cabbage, very thinly sliced (1 pound or 5 to 6 cups shreds) which will be easiest on a mandoline if you have one
4 medium carrots, peeled into ribbons with a vegetable peeler
5 lacinato kale leaves, ribs removed, leaves cut into thin ribbons
4 scallions, thinly sliced on an angle
1 teaspoon kosher salt
1/2 cup all-purpose flour
6 large eggs, lightly beaten
Canola, safflower or peanut oil for frying
Tangy Sauce
1/4 cup ketchup
1 1/2 tablespoons Worcestershire sauce (note: this is not vegetarian)
1/4 teaspoon dijon mustard
1 tablespoon rice cooking wine or sake
1 teaspoon soy sauce
1 tablespoon honey (use 2 if you like a sweeter sauce)
1/8 teaspoon ground ginger
Make the pancakes: Toss cabbage, carrot, kale, scallions and salt together in a large bowl. Toss mixture with flour so it coats all of the vegetables. Stir in the eggs. Heat a large heavy skillet on medium-high heat. Coat the bottom with oil and heat that too.
To make a large pancake, add 1/4 of the vegetable mixture to the skillet, pressing it out into a 1/2- to 3/4-inch pancake. Gently press the pancake down flat. Cook until the edges beging to brown, about 3 minutes. 30 seconds to 1 minute later, flip the pancake with a large spatula. (If this is terrifying, you can first slide the pancake onto a plate, and, using potholders, reverse it back into the hot skillet.) Cook on the other side until the edges brown, and then again up to a minute more (you can peek to make sure the color is right underneath).
To make small pancakes, you can use tongs but I seriously find using my fingers and grabbing little piles, letting a little batter drip back into the bowl, and depositing them in piles on the skillet easier, to form 3 to 4 pancakes. Press down gently with a spatula to they flatten slightly, but no need to spread them much. Cook for 3 minutes, or until the edges brown. Flip the pancakes and cook them again until brown underneath.
Regardless of pancake size, you can keep them warm on a tray in the oven at 200 to 250 degrees until needed.
If desired, make okonomiyaki sauce: Combine all sauce ingredients in a small saucepan and let simmer for 3 to 5 minutes, until smooth and thick.
Serve pancakes with sauce and any of the other fixings listed above, from Japanese mayo to scallions and toasted sesame seeds.
Do ahead: Extra pancakes will keep in the fridge for a couple days, or can be spread on a tray in the freezer until frozen, then combined in a freezer bag to be stored until needed. Reheat on a baking sheet in a hot oven until crisp again.

Buckwheat Noodles with Brown Butter and Cabbages

Katie recommends this quick recipe from Deborah Madison's The Savory Way:

6 T. brown butter
2 garlic cloves, minced
1/2 pound Brussels sprouts, the leaves separated
1/4 cup water
salt
1 pound nappa cabbage, thinly sliced
10-12 oz. buckwheat noodles
3T. chopped parsley
1 bunch of scallions, including some of the green part, sliced into rounds
1/4 cup Gruyere or Fontina cheese
1 T. roasted black or white sesame seeds
freshly ground pepper

Bring a large pot of water to a boil for the pasta and prepare the vegetables while it is heating.

Heat 2 T. of the butter in a wide skillet, add the garlic and Brussels sprouts leaves, and cook over medium heat, turning the leaves frequently until they begin to shine, after a minute or two. Add the water and a little salt and cook until the leaves are sweet and tender, about 3-4 minutes more. Add water, if needed, in small increments. Once the sprouts are cooked, add the cabbage and cook until it's wilted. Season with salt and set aside.

Salt the past water, then add the pasta. When done, drain and add it directly to the vegetables. Add the remaining butter, parlsey, scallions, cheese and sesame seeds, and combine gently. Season with pepper and serve.