Season chicken with 1/4 tsp each of salt and pepper.
Dredge chicken in flour, shake off excess.
Heat vegetable oil in large skillet over medium heat.
Add chicken and cook, turning once after 6-8 minutes. Should be lightly browned on both sides and barely firm when you press the centers of the chicken.
Remove chicken from chicken and set aside.
In same skillet, heat butter over medium heat. Add button mushrooms, stirring occasionally, cook about 6 minutes or until liquid evaporates.
Stir in shallots and cook 2 minutes.
Stir in ground porcini mushrooms and Marsala wine. Increase heat, boil for 1 minute. Add chicken broth and return to boil.
Add chicken breasts; turn to coat in sauce.
Simmer until sauce thickens.
Transfer to serving plates.
NOTE: You can find dried mushrooms in the ethnic foods aisle in your grocery store. I have also found them in the produce department. Once I couldn't find the dried porcini mushrooms so I bought a mix of dried mushrooms. Then I put the dried mushrooms in my spice grinder to grind. I'm sure if you didn't have a spice grinder, you could use a clean coffee grinder or food processor.