To begin, start heating a pot of salted water for your pasta. You’re going to cook a pound of Gamelli or similar pasta while you are making the chicken.
In a small dish, combine the dry mustard and thyme. Set it aside for now.
Cut up the chicken breasts into 1 inch pieces and give them a nice salt & peppering. Heat oil in a large skillet and cook the chicken over medium high heat until golden and cooked through. Remove it to a dish and toss it with the mustard & thyme.
In your skillet, sauté the onion and garlic. Cook them until they are tender and then reduce your heat (or turn it off); whisk in the Cognac (or white wine) to deglaze your pan.
Add in the butter and return this to medium heat. When the butter is melted, whisk in the flour. Cook that for just a minute and then whisk in the whole milk. Stir in the whole grain Dijon mustard and let this cook on medium heat until the sauce just begins to bubble, whisking often.
While that is cooking, grate your cheeses. When the sauce has begun to bubble and is thickened, stir in the chicken, along with the oregano, and crushed red pepper flakes. Finally, whisk in your grated cheeses, stirring until it is completely melted.