Add walnuts and two tablespoons oil to food processor and blend until smooth.
Heat remaining two tablespoons oil in saute pan. When hot, add onions, mushrooms, basil, garlic, salt, and pepper. Cook until browned.
Add mushroom mixture to walnut puree. Blend until smooth.
Scoop pate onto shaved beet round and fold in half. Alternately, place pate between two beet rounds.
Garnish with basil and serve.