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1
Halfway fill a medium bowl with cold water and add a cup of ice.
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2
Preheat the oven broiler with the rack set 4 to 5 inches from the flame or element.
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3
Toast the bread under the broiler until deep golden brown on one side, 1 to 2 minutes.
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4
Transfer to a dinner plate.
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5
In a small saucepan set over high heat, bring a quart of water to a boil.
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6
Using an egg pricker or a thumbtack, carefully poke a hole just through the egg shell on the rounder end.
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7
Use a slotted spoon to carefully lower the egg into the water, along with the potato cubes.
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8
As soon as the water returns to a boil, decrease the heat to medium-low or low so that the water is barely bubbling.
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9
Cook the egg and potato together for 8 minutes (for a slightly soft yolk in the very center) or 9 minutes for a fully cooked yolk.
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10
Use a slotted spoon to transfer the egg and potato cubes to the bowl of ice water.
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11
When the egg is cool enough to handle, scoop it out and crack it all over against the countertop.
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12
Remove a piece of shell from the rounder end and return the egg to the water.
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13
After a minute or two, slip off the rest of the shell and transfer the egg to a cutting board.
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14
When it cools, coarsely chop it and transfer it to a medium mixing bowl.
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15
Scoop the potato pieces out of the water and transfer them to the bowl.
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16
Add the tuna, olives, and 1 tablespoon of the mayonnaise to the bowl and stir to combine, adding up to another tablespoon of mayonnaise if you want a creamier mixture.
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17
Lightly season with salt and pepper to taste.
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18
To assemble the sandwich, sprinkle the spinach leaves onto the toasted side of one of the slices of bread, and top with the tuna-egg-potato salad and the other slice of bread, toasted side facing inward.
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19
Cut in half and eat.
