Put the flours and salt in the bowl of a food processor.  Beat the eggs in a bowl with a fork.  With the food processor running, add the beaten eggs in a steady stream.  Process until the dough comes together and is smooth and elastic, about 4 minutes.  If the dough seems sticky, add a little more flour.  Put the ball of dough in a bowl and cover with plastic.  Let rest 20 minutes.

Divide the dough into 6 pieces.  Cover 5 of the pieces with plastic.  Flatten the remaining piece of dough slightly with your hand, dust it the with flour and crank it through a manual pasta machine with the rollers set at their maximum distance apart, the setting labeled “1”.

Fold the dough in thirds as though you were folding a sheet of typing paper.  Run the dough through the machine again, feeding the narrow side into the rollers.  Repeat the process of folding and rolling 5 or 6 more times.  This process kneads the dough and prepares it for the next step of thinning it.  Don’t hesitate to sprinkle the dough with flour as you continue running it through the machine.  You don’t want it to stick to the rollers. 

Gradually roll the dough to the desired thinness, narrowing the distance between the rollers with each pass of the dough.  If the dough tears just patch it back together and roll it through the same setting again, a little slower this time.  If the dough sticks to the rollers, sprinkle it with flour.  Bring the dough down to the thinnest setting. 

Cut half the pasta sheets into sheets 12” by 7”.  Save the remaining pasta sheets for another use.  Transfer to a board or a sheet pan covered with a towel lightly dusted with semolina. 

Preheat the oven to 250°. Cut the tomatoes in half lengthwise.  Toss the tomatoes in a bowl with the remaining ingredients. 

Arrange, cut-side down, in a single layer on a rack sitting in a shallow roasting pan.  Roast plum tomatoes for 4 hours.  Begin checking after half the cooking time, then every 30 minutes.  They’re done when the edges curl and the skin wrinkles, but they should still be juicy at heart.  Let cool.

Remove the skin from the tomatoes and slice into 0.25-inch strips.  Put in a small saucepan, season with salt and pepper and heat over a low heat when ready to serve. 

Trim the roots and wash and dry the each of greens separately.

Bring a large pot of water to a boil.  Season with salt.  Add the spinach and blanch for 1 minute.  Scoop out plunge into ice water.  Repeat with the basil leaves and the arugula.

Drain greens, but do not squeeze too much water out.

Put greens and garlic in the blender to puree.  Add warm water if needed to keep the greens churning. When the sauce is smooth, add the butter and season with salt and pepper to taste. Reheat over low heat when ready to serve.

Bring a large pot of salted water to a boil.  Add the pasta and cook for 2 minutes.  Scoop out the pasta and dump into the bowl with the cheese mix.  Add the slow-roasted tomatoes and a little pasta water to loosen the cheese and toss well. 

Put a spoonful of green sauce in the bottom of 4 warm pasta bowls.  Put a quarter of the pasta on top of each one.  Garnish with basil and serve immediately.