To make pesto:
1. Pulse garlic in a food processor until finely chopped, then add nuts, cheese, a large handful of basil, and pepper and process until chopped.
2. Add remaining basil one handful at a time, pulsing after each addition, until finely chopped.
3. With motor running, add oil and blend until incorporated.
4. Reserve 5 tablespoons of pesto for the soup and tartines. The remaining pesto can be stored, covered with a thin layer of olive oil, in the refrigerator for up to a week.
To make soup:
1. In a medium saucepan, bring chicken broth and 2 cups water to a simmer.
2. Add onion, carrot, celery, salt, and pepper and simmer, covered, until vegetables are tender, about 6 minutes.
3. Add peas and simmer, uncovered, until peas are bright green and tender, about 3 minutes.
4. Stir in 4 tablespoons of the pesto, then puree soup in two batches in a blender until smooth.
5. Season to taste with salt.
To make tartines:
1. Spread goat cheese on baguette slices, top with a dollop of the remaining 1 tablespoon of pesto, and serve with the soup.