Place the bread on a cutting board, butter one side of each slice, turn over and spread the grainy mustard on the other side. Place a slice of Cheddar cheese on top of the mustard, on each slice. Have the diced ham and spinach ready.
Lightly whisk the eggs with the milk or water and season lightly with salt and pepper. Heat an 8-inch (20 cm omelette pan over medium-high heat and add a touch of butter to the pan. Pour the eggs and, using a silicone spatula, quickly stir the eggs vigorously in small circular motions, keeping the eggs moving. Once they just begin to set, stop stirring and spread the eggs out evenly in the pan. Use the spatula to loosen the omelette around the edges. Sprinkle the ham and spinach leaves over top. Once the omelette is set (about 90 seconds), fold it in half in the pan and then flip it out directly onto one of the prepared bread slices. Top with the other bread slice.
Wipe out the omelette pan and return it to medium heat, or preheat a Panini press. Place the sandwich into the pan or onto the press and press (if using a pan, place a lid on the Panini to weight it) and cook until the bread is toasted and golden, about 3 minutes per side. Slice in half and serve.