In a large wok or skillet, heat 1/2 cup coconut milk over medium-high, stirring, until shiny and thick, about 2 minutes.
Add curry paste and cook, stirring it until fragrant (about 1 minute). Add remaining coconut milk, broth, fish sauce, and brown sugar and bring to a simmer. Add bell pepper and cook until softened (about 2 minutes).
Add baby corn and asparagus, cook until crisp-tender (about 3 minutes).
Add the steak and cook, stirring, until just cooked through, 2 minutes.
Serve over noodles with lime wedges, sliced green onions, and chopped cilantro.