Preheat the oven to 400˚. Toss the bread pieces on a baking sheet with 1 tablespoon olive oil, a pinch of salt and a few grinds of pepper. Roast, tossing halfway through, until browned and crisp, 15 to 20 minutes.
Meanwhile, bring a large pot of salted water to a boil. Fill a large bowl with ice water. Add the green beans to the boiling water and cook until bright green and just tender, 4 to 6 minutes. Drain and transfer to the ice water to cool completely. Drain again and transfer to a paper towel–lined baking sheet; pat dry.
Make the dressing: Puree the anchovies, vinegar, lemon juice, garlic, parmesan and mustard in a blender, scraping down the sides with a rubber spatula, until smooth. With the machine running, slowly drizzle in the remaining ¼ cup olive oil and blend until combined. Season with salt and pepper.
Combine the green beans, kale and half each of the croutons and pepitas in a large bowl. Add the dressing and toss to coat; season with salt and pepper. Transfer to a serving dish and top with the remaining croutons and pepitas; sprinkle with more parmesan.