For a softer ground beef texture, soak the walnuts in a bowl covered by fresh, cold water for at least 1 hour or overnight. This step is optional, so the walnuts can still be blended without soaking.
Heat the olive oil in a large stainless steel sautée pan over medium heat.
Caramelize the tomato paste by sautéing it the olive oil over low heat for 5 minutes to enhance the flavor.
Roughly chop the onions, carrots, and mushrooms into about 1" pieces and place in food processor. Process on low speed until finely chopped, being careful not to over-process.
Add the vegetables to the pan with the caramelized tomato paste and sauté everything together for about 10 more minutes until the veggies start to brown.
While the mixture is cooking, process the walnuts in the food processor until very finely chopped, but do not let it turn into a paste. It should resemble the texture of ground beef
Add the finely chopped garlic to the pan and cook for 1 minute.
Add the ground walnuts and the spices to the sautée pan with the mushroom mixture and stir well. Continue to stir over low heat for 5 minutes.
Add 1/4 to 1/2 cup of water to the pan. The addition of water during cooking will help to incorporate the spices into the mixture and will keep the it from becoming too dry.
Continue to stir for another 5 minutes. Remove pan from heat and place into a serving bowl.