Heat a skillet over medium heat and add the dried peppers. Toast until the peppers start to blister, darken in color, and are fragrant; 3-4 minutes. Turn on your oven vent; if you have it for this, the pepper smell can be a bit nose-tingling once the peppers are toasted, set aside to let cool enough to handle.
Once the peppers are cool enough to hand, remove the seeds (and wash your hands after). Bring a pot of water to a boil, remove from the heat, add the peppers, cover, and let sit for about 10 minutes. The peppers should be soft after this time.
Wipe out the skillet you used to toast the peppers and return to medium heat. Add the cumin and coriander seeds. Toast for about 2 minutes, shaking the pan often. The spices should be darker in color and fragrant. Transfer to mortar (or a high-speed blender if you have it). Grind the spices.
Again, return the skillet to the heat and add 2 teaspoons of the olive oil. Peel and crush each garlic clove then add to the skillet. Cook until the garlic is mostly golden. Turn off the heat and stir in the tomato paste. Let cook in the hot pan, stirring to cook the tomato paste a bit and incorporate with the olive oil.
Finally, remove the soaking peppers from the pot and shake off excess water. Add to a blender/food processor along with the ground spices, garlic mixture, lemon juice, vinegar, paprika, and salt. puree until the mixture starts to come together and begin to drizzle in the olive oil. Puree until mostly smooth, adding a bit more olive oil if needed to help the machine run.
Transfer to a jar, top with extra oil to keep the top fresh, and store in your refrigerator to use within a couple of weeks or freeze for use later.