Bring a large pot of water to a boil. Add a splash of extra-virgin olive oil, add the soba noodles, and cook until just tender, about 10 minutes. Drain the noodles, rinse under cool running water to stop cooking, and set aside.
While the noodles cook (or immediately after draining), whisk together the almond butter and the water in a small bowl until smooth. Whisk in the rice vinegar, then the soy sauce. Set the sauce aside.
Heat a splash of extra-virgin olive oil in a large sauté pan or wok over medium-high heat. Add the broccoli florets, thinly sliced red bell pepper, and shredded cabbage. Sauté, stirring frequently, until the vegetables are crisp-tender, about 4–5 minutes.
Add the minced garlic and minced fresh ginger to the pan and cook, stirring constantly, until fragrant, about 30–60 seconds.
Add the drained soba noodles to the pan with the vegetables. Pour the prepared almond butter sauce over the noodles and vegetables and toss or stir until everything is evenly coated and heated through, about 1–2 minutes.
Remove the pan from the heat. Add the sliced scallions and the almond slivers, and toss to combine. Sprinkle crushed red pepper flakes to taste, if using.
Serve immediately.