To prepare dressing, combine first 7 ingredients, stirring with a whisk.
To prepare salad, place green beans into a large saucepan of boiling water; cook 5 minutes. Drain and plunge beans into ice water; drain. Place beans in a large bowl. Add tomato, dill, and navy beans; toss to combine. Drizzle with dressing; toss gently to coat. Sprinkle with cheese. Cover and chill at least 1 hour.