In a blender or food processor, add 1 tablespoon oil, garlic, ginger, brown sugar, coriander, cumin, mustard, cayenne, turmeric, and vinegar; process until mixture is smooth; set aside.
Heat the remaining oil in a skillet over medium-high heat.
Add in the onion and carrot, cover and cook for 5 minutes or until softened.
Transfer the onion and carrot to a 4-quart slow cooker on LOW heat setting.
Add in the spice paste, stir and cook for 1 minute.
Add in the next 4 ingredients; stir to combine.
In a small bowl, mix together the tomato paste and water; add to the slow cooker along with salt and pepper to taste; cover and cook on LOW for 6 hours.
Add in the peas; cook for 10 more minutes to allow them to heat; serve.