Heat oven to 450 F.
Cut the tops off of the heads of garlic and brush will the oil.
Wrap each head of garlic with foil.
Roast until soft, 1 hour.
Let cool and squeeze roasted garlic cloves from the their skins into a a bowl and mash with a fork to a paste.
Melt 2 tablespoons of the butter and add to the garlic paste.
Then add the milk, parsley, basil, salt, and eggs; stir until smooth.
Place the flour in a large bowl and form a well in the center.
Slowly pour the garlic-milk mixture into the well, and then stir it all together with a fork, until a smooth batter forms.
Bring a pot of salted water to a boil over high heat.
Set the spaetzle maker (or colander) over the pot and working in batches, scrap the batter through the holes into the water.
Cook until the dumplings rise to the surface, about 1 minutes.
Using a slotted spoon, transfer the dumplings to a baking sheet or platter.
Heat the remaining 4 tablespoons of butter in a large skillet over high heat.
Add the dumplings and cook, stirring often, until lightly browned, 6 - 8 minutes.
Add the dumplings to an oven-proof dish (or skillet) and sprinkle the cheese over the top.
Broil on high until cheese melts and just starts to brown, about 2 minutes (keep an eye on it!).
Garnish with parsley.