Place a large skillet in the oven and to 325°F.
Peel the eggplant and discard the skin.
Slice the eggplant lengthwise and scoop out the seeds and surrounding pulp.
Coarsely chop the seeds.
Place 2 teaspoons of the olive oil in the skillet. Place the chopped eggplant seeds on one side of the pan and the diced shallot on the other side.
Return the pan to the oven and cook for about 15 to 20 minutes. Stir occasionally, keeping the eggplant and onions separated.
Remove and let cool.
Place the roasted eggplant seeds in a blender or mini-chopper. Add the salt, pepper, and 1/2 teaspoon of the smoked paprika.
Process by pulsing the blender or mini-chopper until the mixture is a coarse paste.
Place in a bowl, then add the remaining 2 teaspoons olive oil and the roasted shallot.
Fold together and chill.
Cut the remaining eggplant into 1/4 inch dice.
While the eggplant seeds and onions are roasting, place the water in a medium sauce pan over high heat.
When the water is at a simmer, add the diced eggplant and poach for 4 minutes.
Remove the eggplant to a paper towel and pat dry.
Place the eggplabt in a bowl with the lemon juice and toss well. Immediately place in the refrigerator to cool.
When the eggplant and onion mixture is chilled, fold together with the chilled diced eggplant.
Chill.
Dust one side of the tuna steaks with the remaining 1/2 teaspoon smoked paprika.
Place a skillet over medium high heat and add two teaspoons olive oil.
When the oil is hot, place the tuna in the pan paprika side down.
Sear for about 3 minutes.
Grind the black pepper over the top of the tuna and turn.
Cook for three minutes.
Remove and chill.
When ready to serve, divide the eggplant tartare between two plates and top with the tuna steak.