Place porcini mushrooms into a medium heatproof bowl and cover with hot water. Set aside to soak for 20-25 minutes or until soft. Drain well.
Heat 2 tbsp oil in a medium frying pan over medium heat. Add garlic and cook, stirring occasionally, for 2-3 minutes or until light golden. Stir in drained porcini mushrooms and cook for 5-6 minutes or until just tender. Remove and place into food processor bowl.
Add 1/4 cup oil and button mushrooms to the pan and cook, stirring often, over high heat for 5 minutes or until golden around the edges and tender. Remove and add to mushrooms in processor bowl. Add lemon juice, salt, pepper, tarragon and remaining oil to mushrooms. Process until mixture is finely chopped (do not puree).
Spoon into a medium sterilized jar. Drizzle with a thin layer of extra oil to completely cover tapenade. Place lid onto jar, cover jar with a tea-towel and set aside to cool completely before sealing.
Recipe yields 1.5 cups.