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1
First, make the pasta dough (unless you'd rather just buy sheets of fresh pasta-that's ok too!). Dump the flour and salt onto a clean countertop or large cutting board and make them into a mound with a big well in the center. Beat the 2 eggs with the 2 tablespoons of water and pour into the well in the dry ingredients. Slowly mix in the flour with a fork, working around the edges of the well so as to keep the liquid confined; when it starts to get sticky, use your hands to mix. Knead the dough, with extra flour or water as necessary, until it's smooth and elastic (it will take a while). When it's good and springy, cover it with plastic wrap or an upside-down bowl, and leave it to rest while you make the filling.
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2
Start with the leeks: chop off the greens and the roots, and halve the white parts lengthwise. Wash them well and carefully to make sure there's no grit trapped between the layers, then chop them up. For the artichoke hearts, if you start with fresh artichokes, here's a handy tutorial for cleaning them up: http://moroccanfood.about.com/od/tipsandtechniques/ss/artichoke_clean.htm Don't toss the stems, if your artichokes have them-you can peel them and use the inner parts just like the rest of the heart! Coarsely chop the hearts once they're all cleaned.
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3
Heat some olive oil in a pan and saute the leeks until they soften. You don't want them crisp, so keep the heat medium-low. Add the artichoke hearts and a bit of water, and cover the pan to let them steam a bit. When the artichokes are soft, take the pan off the heat and put the leeks and artichokes in a bowl to cool a bit.
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4
While the vegetables are cooling, it's time to roll out the pasta! Divide your dough in half and roll it out, either using a pasta machine or a rolling pin (for some good tips on how to get thin pasta without a machine, try here: http://lacucinaitalianamagazine.com/articles/how-to-hand-roll-pasta-dough)
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5
Lay out one sheet of pasta and dollop on the filling with enough space in between spoonfuls to seal the ravioli. Mix the egg white with the 2 teaspoons of water and brush it around the filling; then, cover the whole thing with the second sheet of pasta and carefully seal off your ravioli one by one. Try not to get air bubbles around the filling. Once they're sealed up, cut your ravioli apart. At this point, you could freeze them and keep them to cook another time-but why wait? Instant (or nearly so) leek-and-artichoke gratification awaits! Cook them in boiling, salted water for 3-6 minutes, or until the pasta is as done as you like (the time will depend on how thick you rolled your dough out). Serve with your favorite sauce (I often just heat up a can of crushed no-salt tomatoes and mix in any extra filling to make a sort of pink sauce), hot out of the pot.
