Start by getting a huge pot of water boiling and add a handful of salt. Have a large bowl with ice water in it nearby.
Toss the ramp leaves into the boiling water. Stir around and boil for 2 minutes. Fish them out with a skimmer or tongs and immediately dump them into the ice water. Once they are cool, put them in a colander to strain.
Chop the ramp leaves roughly and put them in a blender. Add about 1/2 cup of the ice water to the blender and puree. Ramp leaves can be stringy, so blitz the hell out of them for a solid 90 seconds. Pour the contents of the blender into a fine-meshed strainer set over a bowl. Let this drain for a minute or two.
Put the flour in a large bowl and make a well in the center. Add the ramps from the strainer and begin mixing the dough with a fork. It should come together as a pliant dough, but if it looks like it will be a little to firm, add a splash of the green water from the straining bowl. Once you get a shaggy mass, start working the dough with your hands. Knead it on a floured surface for 5 minutes. Cover the dough with a thin film of olive oil and wrap in plastic. Let it sit for an hour or so to hydrate.
Cut the dough into 6 equal pieces. Cover the rest while you work with each one. Roll the dough out in a pasta machine; I use an Atlas pasta maker. Roll it out to No. 4 on the machine, which is about 1/8 inch thick or so -- not too thin. Dust the pasta sheet with some flour and run it through the spaghetti cutter that comes with the Atlas. Dust the ramp pasta with flour again and set it on a baking sheet or wooden board to dry. Repeat with the rest of the dough.
The pasta will sit like this for up to a day. Boil in lots of salty water until they float, and then for another minute or two. Serve at once with the morel ragout.
Wash the morels and slice them into disks. Separate the ramp bulbs from the leaves. Chop the bulbs and slice the leaves in halves or thirds, depending on how large they are.
Arrange the morels and chopped ramp bulbs in a saute pan. Turn the heat to high. Once the morels begin to release their water, turn the heat down to medium-high and sprinkle some salt over everything. Sprinkle the caraway over the pan now.
When the morels have released most of their liquid, add 2 tablespoons of the butter and stir to combine. Saute the morels and ramp bulbs until the begin to brown, about 3 or 4 minutes. Add the chicken stock and use a wooden spoon to scrape up any browned bits at the bottom of the pan. Boil this down by half over high heat.
When the ramp pasta is just about ready, add the remaining ramp leaves to the saute pan and cook them 1 minute, until they are just wilted. Put the finished pasta into the saute pan with the remaining butter and gently mix to combine. Grind some black pepper over everything and serve at once.