Preheat the oven to 300°F (150°C). Brush both sides of each slice of baguette with 2 tbsp olive oil. Season with salt and pepper. Spread on a baking sheet. Bake for 15 minutes, or until crisp and golden.
Meanwhile, cook the fava beans in boiling water for 2 minutes. Drain and rinse under cold running water. Reserve a few beans for garnish. Purèe the remaining beans in a food processor with the shallot, garlic, the remaining 1 tbsp olive oil, and the tarragon leaves. Season to taste with salt and pepper.
Just before serving, spread the fava bean paste onto the prepared crostini. Garnish with the reserved beans and a sprinkling of black pepper.