In a large skillet, heat the olive oil over medium heat. Add the diced onion and chopped carrot, cooking until the onion is translucent and the carrot begins to soften, about 5-7 minutes. Stir in the grated ginger and minced garlic, cooking for an additional minute until fragrant.
Add the tomato paste, garam masala, ground turmeric, chili powder, paprika, cumin, and cayenne pepper to the skillet. Stir well to coat the vegetables in the spices, allowing them to toast slightly for about 2 minutes.
Introduce the cauliflower florets to the skillet, stirring to combine with the spiced mixture. Pour in the vegetable broth and the diced tomatoes (with their juices). Bring the mixture to a gentle simmer, then cover and let it cook for about 10 minutes, or until the cauliflower is tender.
Once the cauliflower is cooked, add the chickpeas and coconut milk to the skillet. Stir well and let it simmer uncovered for another 5 minutes, allowing the flavors to meld together beautifully. Finish with a splash of fresh lemon juice for brightness.
Remove the skillet from heat and sprinkle with chopped fresh cilantro, if desired. Serve your Vegetarian Tikka Masala warm, alongside fluffy basmati rice and warm naan bread for the ultimate dining experience.