Heat a dry skillet over medium heat and add the slivered almonds, stirring frequently for 3-4 minutes until fragrant and lightly golden. Transfer to a plate to cool completely—this brings out their nutty flavor and ensures maximum crunch. While the almonds toast, chop the broccoli into bite-sized 1/2-inch pieces and thinly slice the green onions. This is the perfect time to prep everything so you can move quickly once you start assembling the slaw.

In a small bowl or measuring cup, whisk together the olive oil, sugar, soy sauce, and rice vinegar until the sugar dissolves completely and the mixture is well emulsified. The vinegar and oil will want to separate, so whisking is key to getting them to combine temporarily—they'll naturally separate again as it sits, which is fine. I like to taste the dressing at this point and adjust the balance; if it feels too acidic, a touch more sugar helps, or more soy sauce if you want deeper umami flavor.

Place the cabbage mix in a large mixing bowl and add the chopped broccoli and sliced green onions. Pour the dressing from Step 2 over the vegetables and toss well until everything is evenly coated. The cabbage will start to soften slightly as it sits in the dressing, which is exactly what you want—it becomes more tender and absorbs all those flavors.

Crush the ramen noodles into small chunks directly into the bowl—don't cook them; the raw noodles stay crunchy and absorb just enough dressing to flavor themselves without becoming soft. Add the cooled toasted almonds from Step 1 and sprinkle the sesame seeds over top, then toss everything together until evenly distributed. The key to keeping this slaw crispy is adding the noodles and almonds at the last moment rather than letting them sit in the dressing too long.