Preheat oven to 350°. Spray a 1 1⁄2-quart baking dish with nonstick cooking spray. Set aside.

In a large saucepan, cook beans in boiling water until crisp-tender, approximately 3 minutes. Drain, and set aside.

Add butter to saucepan; melt over medium heat. Add 4 tablespoons flour; whisk 1 minute. Whisking constantly, add milk, broth, 3⁄4 teaspoon salt, and pepper. Bring to a boil; cook, stirring constantly, 2 minutes. Place beans and almonds in prepared dish; pour sauce over beans.

Bake until beans are tender, 25 to 30 minutes.

In a medium skillet, heat oil over medium-high heat. In a shallow bowl, add remaining 3 tablespoons flour and shallot, tossing to combine.

Shake excess flour from shallot; place in hot oil. Cook, turning occasionally, until golden brown, 2 to 3 minutes. Drain on paper towels; sprinkle with remaining 1⁄4 teaspoon salt. Top casserole with fried shallot.