In a small bowl, whisk together the garlic, salt, oregano, and pepper.
Heat the oil in large skillet over medium heat. Add the tomato paste and paprika and saute for 2 minutes. Add the onions and carrots and saute until softened. Stir in the spice mixture and sliced mushrooms. Cook for 10 minutes, stirring frequently.
Meanwhile, place the chopped tomatoes and chipotle chili pepper in a blender and blend on high until smooth.
Add the tomato mixture to the pan with mushroom mixture. Reduce the heat to medium-low and cook until the liquid has been reduced to about one-fourth its original volume and has the consistency of pulled chicken.
Notes
Test Kitchen Notes: Make sure to cut the mushrooms and onions into thin strips to mimic pulled or shredded meat. Be sure to cook the sauce down until it's thick and a bit "clingy." This concentrates the flavor and helps to provide the look and feel of shredded meat.