Bring a large pot of lightly salted water to a boil. Cook udon noodles in boiling water, stirring occasionally, until noodles are tender yet firm to the bite, 10 to 12 minutes. Drain and rinse under cool water; set aside.

Whisk together gochujang, 1/4 cup water, soy sauce, maple syrup, and lime juice in a bowl. Set sauce aside.

Heat oil in a wok or large skillet over medium-high heat until shimmering. Add kale, 1/4 cup scallions, garlic, salt, and pepper. Cook, stirring constantly, until greens are just wilted and tender, and garlic and scallions are glossy and almost translucent, about 2 minutes.

Add sauce to greens and cook until slightly thickened and darkened in color, about 1 to 2 minutes.

Add cooked noodles and cook until sauce is bubbling, about 2 to 3 minutes, gradually adding remaining 1/4 cup water if more sauce is needed to coat the noodles.