You could make gnocchi with 4 cheese sauce, which is one of my favorite, all though quite a heavy dish. Another heavy but favorite of mine are pizzoccheri, which are traditionally made with a cheese called bitto, but I can't always find it in my region and sub it with fontina, but I think any flavorful cheese that melts would do the trick. Pizzoccheri are rectangular shaped buckwheat pasta, if you can't find real pizzoccheri, I bet you could find some form of buckwheat pasta. Remember, I warned this is NOT a low-fat dish... They eat it in the winter in the Alps
500g of your unidentified cheese
150 g parmigiano (or grana/substitute)
2-4 cloves of garlic
Cut the potatoes in cubes, about 1 inch.
Slice the cabbage (I usually put more cabbage in there because I like it, and when boiled it really goes down substantially, I would put 1 small head of cabbage-500-600 grams)
Grate the parmigiano and cut your chease into small, meltable pieces.
Peel the garlic (you can slice one side of it or cut the cloves in half if you want to get more juices out), put it in a small saucepan with the butter, leave out to soften and mix their flavors.
Put a large pot on to boil. When the water boils, add rock salt (3 handfulls or so)
Add the potatoes and the cabbage, after 5 min the pizzoccheri (depending on your buckwheat pasta cook-time. This is based on 12-15 min pizzoccheri cook-time)
As the pasta cooks, turn the heat on really really low under your butter/garlic, you just want your butter to melt.
When the pasta is done, drain the pot (potatoes, cabbage and pasta)
In a bowl/dish, put one layer of pasta mix, sprinkle on top some of both cheeses, dump on some melted butter (remove the whole garlic pieces from the butter before using)
Repeat layering until all ingredients are finished. Mix well and serve hot.
As far as what to do with your eggs, you can always make egg pasta, you can dry it and freeze it and it keeps really well.