Remove stem and seeds from the dried chiles. Using a skillet over medium-high heat (or the fire from your gas stove) toast the chiles for 1-2 minutes, flipping to toast evenly. Cut the chiles in about 2-inch pieces and place in a microwave-safe bowl with 3 cups of water. Microwave for 5-6 minutes, stopping to stir and check every couple of minutes. The chiles will reconstitute and become soft. Set aside (reserving liquid!).
In a large skillet, heat olive oil over medium heat. Add onion, cook for 2 minutes, and add garlic. Stir in kosher salt, chili powder, cumin, oregano, black pepper, and tomato paste. Remove chiles from the liquid (still reserving the liquid) and add them to the skillet. Add 1 1/2 cups of chili liquid and stir to combine.
Remove from heat and either cool slightly to add to blender, or use an immersion blender to blend together until smooth. Pour sauce through a fine mesh strainer (you may need to use a spoon to "squeeze" the liquid out. Return the sauce to skillet and simmer for 3-4 minutes to continue to enhance the flavor. Remove from heat and set aside to use as desired.