Heat 1 tablespoon olive oil in a large saucepan over medium heat. Cook and stir red onion in the hot oil until fragrant, about 1 minute. Add butter, lemon, ginger, garam masala, chili powder, and cumin; stir to coat, about 1 minute.
Stir half-and-half, yogurt, and tomato paste into onion mixture and cook until well mixed and smooth, about 5 minutes.
Heat 1 tablespoon olive oil in a separate skillet over low heat. Pan-fry paneer in the hot oil until slightly brown, about 5 minutes per side. Mix cooked paneer and chickpeas into the spiced cream sauce. Simmer until heated through, about 10 minutes.