Source: HowToCook (a programmer's guide)
Drain the tuna thoroughly — water pooling in the tin will dilute the mayonnaise and turn your filling soggy. Flake it into a bowl and break down any large clumps with the back of a fork. Add the mayonnaise and 10 ml of Russian-style pickle juice (the vinegar sharpens the fish and cuts through richness). Stir until you have a cohesive paste with small, even pieces of tuna visible — not a smooth mousse. Taste and add another 5 ml of pickle juice if the tuna reads flat. This is a cold-preparation step, so you can make the filling up to four hours ahead and refrigerate it.
Lay one bread slice on the panini press and apply a thin layer of the tuna mixture — about 10 ml, spread edge to edge but not quite to the corners. This prevents the filling from forcing out under heat. Layer the ham slice, then the cheese, then the second bread slice. Press down firmly but don't crush. Close the press and heat at a medium setting (not the maximum). The goal is melting the cheese and warming the filling through without scorching the bread exterior, which happens fast with square slices and poor contact.
The press will click or disengage once the surface temperature levels off — usually 3–4 minutes depending on your machine. Open it and check: the bread should have light golden colour with some charring at the edges, the cheese should be fully liquid, and you should smell the tuna warming through without any burnt-bread note. If the cheese is still solid, close and heat for another 60 seconds. Overcooking dries the filling and hardens the bread into cardboard.
Plate straight away. The cheese will be at 70–75°C and will begin to set as it cools, so eating it within two minutes gives you the best texture contrast — warm, yielding cheese against firm bread. If you're preparing this for later — say, as a packed lunch — allow it to cool completely before wrapping, or condensation will make the bread damp.
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