Rinse the basmati rice under cold water until the water runs clear. Place it in a medium saucepan with 3 cups of water and a pinch of salt. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes. Remove from heat and let it sit covered for 5 minutes before fluffing with a fork.
Heat the olive oil in a large skillet over medium heat. Add the diced onion and cook for 5 minutes until it softens and turns light brown.
Stir in the minced garlic and grated ginger. Cook for 1 minute until fragrant.
Add the garam masala, cumin, paprika, and turmeric. Stir for 30 seconds to toast the spices.
Pour in the crushed tomatoes and bring the mixture to a gentle simmer. Cook for 5 minutes, stirring occasionally.
Add the drained chickpeas, coconut milk, and salt. Stir well and simmer for 10 minutes until the sauce thickens slightly and the chickpeas are heated through.
Spoon the rice onto plates or a serving dish. Top with the chickpea tikka masala. Scatter chopped cilantro over the top and serve with lemon wedges on the side.