In small bowl, cover nuts with 1 cup cold water. Set aside for at least 2 hours to soften. For optimal results, soak for up to 7 hours.
Drain nuts well and place in high-speed blender along with remaining pesto ingredients. Pulse, scraping down inside of container, until coarsely pureed. Add water, 2 Tbsp at a time, and pulse until mixture is as smooth and creamy as you like. Add more seasonings to taste, if you wish.
Transfer pesto to airtight container and refrigerate for up to 3 days. Alternatively, pack into ice cube trays and freeze. Once frozen, transfer pesto cubes to sealed container and freeze for up to 1 month. Makes about 2 1/2 cups pesto.
In medium bowl, combine beans and tomatoes. Gently toss together.
To serve, line 4 serving plates with lettuce. Spoon bean and tomato mixture on top. Place a couple of avocado slices on each and top with some pesto. Place poached egg or slice of halloumi on each and another dollop of pesto. Serve immediately.