2 lb beef bottom round, trimmed
2 tsp kosher salt
1 tsp black pepper
1 cup all purpose flour
3 eggs, beaten
1/4 cup vegetable oil
2 cups chicken broth
1/2 cup whole milk
1/2 tsp fresh thyme
Preheat oven to 250F.
Cut meat with the grain into 1/2 inch slices, then season each slice with salt and pepper on each side. Fill one bowl with the flour, then another bowl with the beaten eggs.
Dip the meat on both sides with the flour, then tenderize the meat to about 1/4 inch thick with a meat tenderizer or needling device. Dip again in flour, followed by egg, then flour again. Do this with all pieces of meat and set aside on a plate. Let sit for about 10-15 minutes before cooking.
Place enough vegetable oil to cover a 12 inch skillet and set on medium high. Once the oil begins to shimmer, add the meat in batches, careful to not over crowd the pan. Cook each piece on both sides until golden brown, about 4 minutes per side. Remove from pan, then set aside on a wire rack on a sheet pan and place in the oven. Repeat until all meat is cooked.
Add the remaining vegetable oil to the pan, or at least 1 tbsp. Whisk in 3 tbsp of flour left over from dredging and add the chicken broth.Whisk until gravy comes to a boil and begins to thicken. Add the milk and thyme and wisk until the gravy coats the back of a spoon, about 5-10 minutes.Season to taste and serve over steaks.