Step 1

Cut each chicken breast crosswise into 3 or 4 pieces. Place them, a few at a time, into a gallon-size zip-top plastic bag and pound with a rolling pin to a uniform 1/2-inch thickness. Sprinkle the chicken lightly with salt and pepper.

Step 2

Place the crackers into another zip-top bag and crush with a rolling pin until finely crushed. Place the crumbs into a shallow pan or plate. Place the buttermilk into another shallow pan or plate. Dip each piece of chicken into the buttermilk, then into the crumbs to coat them well on each side. Place on a plate and refrigerate for at least 15 minutes before frying.

Step 3

Heat 5 tablespoons of vegetable oil in a wide skillet over medium-high heat until it sizzles when a bit of the crumb coating is dropped into it. Place a few pieces of chicken at a time into the pan without crowding, and fry for 3 to 4 minutes on each side. Remove to a warm plate and slide into a warm oven while you finish frying the rest of the chicken, adding more oil if necessary.

Step 4

When all of the chicken is cooked through and golden brown, remove it to the waiting plate and immediately add the butter to the empty pan and let it melt, then add the broth, whisking to pick up any browned bits on the surface. Add a cup of half and half and the thyme and continue to whisk until it comes to a boil. Lower heat to a simmer.

Step 5

In a small bowl, create a slurry by combining the cornstarch with the remaining 2 tablespoons of half-and-half, stirring until a light paste is formed. Pour this into the simmering mixture and stir and cook an additional 2 minutes until a smooth gravy is formed.

Step 6

Taste and add salt and fresh ground pepper as necessary.