Preheat the oven to 425 degrees F. Toss the squash with 1 tablespoon olive oil, 1/2 teaspoon salt and a few grinds of black pepper on a baking sheet; spread in a single layer. Roast until tender and browned, about 30 minutes.
Meanwhile, heat 2 tablespoons butter in a large pot over medium heat. Add the leek, carrots, garlic, marjoram, bay leaf, 1 teaspoon salt and a few grinds of black pepper. Cook, stirring occasionally, until the vegetables are tender and golden, about 5 minutes. Stir in the roasted squash, chicken broth and 2 cups water; bring to a simmer. Cook until the carrots are tender, about 20 minutes. Discard the marjoram sprigs and bay leaf. Puree the soup in the pot using an immersion blender until smooth (or puree in a regular blender in batches).
Melt the remaining 3 tablespoons butter in a medium skillet over medium heat. Cook, swirling the pan, until browned, about 5 minutes. Add the browned butter to the soup and puree again; reserve the skillet. Gently reheat the soup over medium-low heat; thin with water if necessary. Season with salt and cayenne.
Wipe out the reserved skillet, add the remaining 1 tablespoon olive oil and set over high heat. Lightly season the shrimp with salt and add to the skillet. Cook, turning once, until the shrimp are browned around the edges, 3 to 4 minutes. Remove to a plate.
Add the almonds to the skillet and toast, stirring occasionally, until golden, about 1 minute. Serve the soup in small cups or bowls. Top with the shrimp, almonds and chives.
The soup can be prepared in advance through step 2; let cool, then refrigerate up to 24 hours or freeze up to 1 week. If the soup separates, puree again before serving.