Sprinkle chicken with 1 tsp. salt and 1⁄2 tsp. pepper. Cook in hot oil in a large sauté pan over medium-high heat, stirring often, 7 minutes or until done. Remove from pan.
Melt butter in pan. Add mushrooms and shallots, and sauté 5 minutes or until mushrooms release their liquid and begin to soften. Stir in thyme and dry mustard. Cook 1 minute.
Remove pan from heat; stir in cognac, and carefully ignite the fumes just above mixture with a long match or long multipurpose lighter. Let flames die down.
Prepare pasta according to package directions.
Meanwhile, return pan to heat; cook over medium heat, stirring often, until liquid is reduced to about 1 Tbsp. Stir in broth, and cook 5 to 7 minutes or until reduced by half. Reduce heat to low, and stir in cream and Dijon mustard. Cook, stirring often, 10 minutes or until reduced by half. Return chicken to pan. Cook 1 to 2 minutes or until thoroughly heated. Sprinkle with remaining 1⁄2 tsp. salt and 1⁄2 tsp. pepper. Pour chicken-and-sauce mixture over hot cooked pasta, and toss to coat. Serve immediately.