Turn the oven on and set the heat to 400 degrees.
Pour the oil on the baking sheet and, using your clean hands or a paper towel, spread it around.
Put the bread crumbs, flour, salt, pepper, and cayenne (if you like it) on the plate. Mix well.
Crack the eggs into the bowl and beat them with the fork or whisk until pale yellow. Add the mustard and thyme and mix well.
Add the chicken pieces and swish them around until they are well coated with the egg mixture.
Remove the chicken pieces, one at a time, from the egg mixture and let any extra egg mixture drip off.
Dip the chicken pieces, one at a time, in the bread crumb mixture, rolling them and pressing down to coat each side.
Shake off any extra coating, then put the chicken pieces on the baking sheet. Be sure to wash your hands with soap and water after handling raw chicken.
Once the oven temperature has reached 400 degrees, put the baking sheet in the oven and bake for 15 minutes. Using a spatula or tongs, turn the chicken pieces over and bake until golden brown, 15-20 more minutes. Serve right away, with a quarter of a lemon on each plate.