Preheat the oven to 350F. Scatter the bread cubes into a single layer on a rimmed sheet pan. Toast for about 8 minutes, shaking the pan from time ti time, or until the bread has dried out to the touch and may have hints of golden brown at the edges of the pan. Take the pan from the oven and let the bread cool on the sheet pan.

Place a heavy-bottomed cast-iron or stainless steel frying pan over medium high heat. Toss in the ham cubes and let the ham cubes sit and fry in the dry pan for about 1 1/2 minutes without stirring. After the 1 1/2 minutes, stir occasionally and fry until the ham is fragrant and has some caramelized edges. Transfer the ham to a plate. Return the pan to the heat and swirl in the olive oil. Add the onion and bell pepper and a pinch of kosher salt. Fry the onions and peppers, stirring frequently, until fragrant and crisp tender. Add the spinach all at once and toss the onions, peppers, and spinach together just until the spinach has wilted and is bright green. Transfer the vegetables to the plate with the ham and allow to cool for about 5 minutes.

Spray a 12-cup standard muffin tin generously with non-stick cooking spray. Set aside.

In a large mixing bowl, beat the eggs, milk, salt, dried mustard, and black pepper together with a whisk until the mixture is an even colour. Switch to a sturdy spoon and mix in the Swiss cheese and cooled bread cubes. Toss in the cooled ham and vegetables until evenly distributed. Use a couple of spoons to divide the soaked bread, ham, vegetables, and cheese between the muffin tin cups. There will be liquid left in the bowl after doing that, so divide that between the muffin cups, too. Bake for 25 to 35 minutes, or until puffed and golden brown on top. The top of the Ham and Egg Muffin Cups should spring back when pressed lightly with your finger.

Let the Ham and Egg Muffin Cups rest for at least 3 minutes before using a thin, flexible spatula or knife to run around the edges of the cups and easing them out. They can be eaten right away or cooled, and stored in the refrigerator for up to 5 days.

For longer storage:

Individually wrap the cooled Ham and Egg Muffin Cups and freeze. Transfer the wrapped, frozen muffins to a zipper top bag. The frozen Ham and Egg Muffin Cups can be reheated by unwrapping, placing on a plate, covering the plate with plastic wrap (leaving a corner vented), and heating for 1 minute in the microwave. If additional heating is needed, heat in 15 second bursts until hot through and through.