Poach chicken breasts in chicken broth or seasoned water until cooked through.

Cool the cooked chicken thoroughly.

Shred the cooled chicken.

Slice the red potatoes.

Place potato slices into salted, boiling water and cook until just tender.

Drain the potatoes.

Grease a casserole dish.

Place the cooked potato slices in the bottom of the greased casserole dish.

Top the potatoes with shredded chicken.

In a saute pan, melt butter.

Add minced garlic and shallot to the melted butter.

Cook the garlic and shallot until softened.

Add flour to the pan and whisk well.

Add chicken broth and whisk until smooth.

Add white wine and half-and-half to the sauce.

Bring the sauce to a boil, stirring constantly.

Add yellow mustard and mayonnaise to the sauce and remove from heat.

Add grated cheddar cheese and Monterey Jack cheese to the sauce and stir until melted.

Season the sauce with salt and pepper to taste.

Pour the cheese sauce mixture atop the chicken and potatoes in the casserole dish.

Bake at 375 degrees Fahrenheit (190 degrees Celsius) for 20 minutes, or until golden and bubbly.