By hand or in a food processor, chop the mushrooms very finely.
In a 12-inch skillet, heat 1/2 tablespoon olive oil over medium-low heat. Add the chopped mushrooms and 1/4 teaspoon of salt. Stirring periodically, allow the mushrooms to cook until all of their natural liquid has released and evaporated, 5-10 minutes. Stir in the Braggs Liquid Aminos and remove the mushrooms from the pan. Set aside.
Wipe down the skillet and add 1/2 tablespoon olive oil, the chopped onion and 1/4 teaspoon of salt. Over medium-low heat, allow the onions to cook until translucent for 3-5 minutes. Turn the heat up to medium and allow the onions to caramelize for several minutes. If the bottom of the skillet starts browning, add a few tablespoons of water to deglaze, incorporating the brown bits into the onion.
Add the garlic and crushed red pepper flakes. Stir and cook for a minute and then add the mushrooms back to the pan.
Stir together the tomatoes, tomato paste and water.
Distribute the lasagna noodles evenly across the skillet and then cover with the tomato mixture. Cover the skillet and allow the mixture to simmer for 20 minutes, stirring occasionally, until the noodles are cooked.
Remove the skillet from the heat and distribute the pecorino romano cheese evenly across the top. Spoon the ricotta cheese evenly over the top and sprinkle with basil. Allow to cool for 5 minutes before serving.