Heat oil in a medium saucepan over medium. Sauté butternut squash 3-4 minutes, stirring often. Add onion and continue to cook with butternut squash 7-8 minutes. Add garlic, ginger, curry powder, and red pepper flakes and cook, until fragrant, about 2 minutes. Add lentils and cook, stirring, 1 minute. Add tomato paste, fresh cilantro, a generous pinch of salt, and broth or water; season with pepper. Set aside ¼ cup coconut milk for serving and add remaining coconut milk to soup. Bring mixture to a boil; reduce heat and simmer gently, stirring occasionally, until lentils are soft but not mushy, 20–25 minutes. Remove soup from heat, season with more salt and pepper if needed, and add arugula; combine well.

To serve, divide soup among bowls. Drizzle with reserved coconut milk and squeeze fresh lime juice. Enjoy!