Add the oil, garlic, and ginger to a food processor. Pulse until a rough, wet paste forms with no large pieces remaining.
Add the Kashmiri chili powder, smoked paprika, ground coriander, cumin, turmeric, and garam masala. Pulse until fully incorporated with no dry streaks.
Add the tomato paste, lemon juice, apple cider vinegar, and salt. Blend until completely smooth, adding water 1 tablespoon at a time if the mixture is too thick to blend.
Transfer the paste to a skillet over medium-low heat. Cook, stirring constantly, for 5 to 7 minutes, until the raw garlic smell fades and the paste darkens by a shade.
Remove from heat and let cool completely at room temperature, about 20 minutes.
Transfer to a clean glass jar, pressing down to remove air pockets, and seal tightly.