Heat the oven to 220°C.
Halve the salmon widthwise then cut each half into 6 equal strips. Sieve the flour over a large plate or bowl. Whisk the eggs in another bowl then tip the breadcrumbs into a third one. Sprinkle each bowl with salt and pepper.
Dip the salmon strips into the flour, then into the eggs and finally into the breadcrumbs. Make sure to coat them evenly.
Shallow-frying: Pour the oil and the butter into a large frying pan and set over medium-high heat. Fry the salmon strips for about 3 or 4 minutes on each side. The strips should be thoroughly cooked, crunchy with a nice golden colour. Remove from the pan and place over kitchen paper to drain.
Baking: Pour a little bit of olive oil on a large baking tray then add the salmon strips. Put in the oven for about 8 to 10 minutes, turning them after 4 or 5 minutes. The strips are ready when golden, crunchy and well-cooked.
Making the tomato dip: Using a food processor or a hand blender, process the chopped tomato until creamy. Sieve the tomatoes over a small saucepan set over low heat. Simmer until the puree has thickened (4-5 minutes).
Set aside to cool down. Once cool, mix in the crème fraîche, basil, salt and pepper.
Serve the salmon fingers together with the tomato dip and lemon wedges.