Preheat oven to 375°. Microwave carrots and 2 Tbsp. water in a microwave-safe glass bowl at HIGH 1 to 2 minutes or until crisp-tender. Drain. Melt butter in a medium skillet over medium-high heat; add onion, and sauté 2 minutes. Add mushrooms; cook, stirring constantly, 2 minutes. Add beans and carrots, and cook 2 minutes. Sprinkle all-purpose flour, salt, and pepper over vegetables. Cook, stirring constantly, 1 minute or until smooth. Gradually stir in broth; cook over medium-high heat, stirring constantly, 8 to 10 minutes or until mixture is thickened and bubbly. Stir in chicken. Stir together self-rising flour and cream just until dry ingredients are moistened. Turn dough out onto a lightly floured surface, and knead lightly 3 or 4 times. Pat or roll dough to 1/2-inch thickness; cut with a 3-inch round cutter to make 4 biscuits, reshaping once, if necessary. (Do not twist cutter as you cut.) Place 4 (10-oz.) ovenproof bowls in a jelly-roll pan. Divide hot chicken mixture among bowls, and top each with a biscuit. Bake at 375° for 20 minutes or until biscuits are golden brown.
Note: We tested with White Lily Enriched Unbleached Self-Rising Flour.