I'm not familiar with that particular Malbec, so I offer two different recommendations depending on the body of the wine. For a full-bodied Malbec, I would recommend a hard Spanish cheese like zamorano, a sharper, nuttier cousin of Manchego. If the Malbec is medium-bodied, the most common pairing is probably morbier (the zing of the cheese complements the fruit in the wine) but it is a stinkier cheese. If you prefer a milder cheese, I suggest robiola (a soft ripened, creamy cheese from Piedmont) or cabecou feuille (chevre soaked in brandy, and wrapped in a chestnut leaf).
The Sangiovese will pair beautifully with piave vecchio (they are a perfect match) or if you want something spicy, try it with pecorino pepato-- it is studded with peppercorns!
IMHO fresh chevre pairs best with a grassy sauvignon blanc to balance the lemon/ tang. Cabecou feuille will pair nicely with a lighter red like Malbec or Pinot Noir because it is sweeter and creamer than fresh chevre. If you have a chevre that is mushroomy and melting, such as Humboldt Fog, then I recommend a big juicy Cab.
Enjoy and please report back on the pairings!
I think your two very safest choices would include Plain Chevre and Parmesan Reggiano... those are musts...
My "2nd tier" would be an aged cheddar. I'd target around 4 to 6 years. I'd also consider this an essential for your wines.
3rd tier choices would include an aged Gouda and Provolone Val Padana. I'd also have a Pecorino Stagianato in this category, all 3 well worth trying but perhaps not as predictable as the Chevre, Parmesan, and Aged Cheddar.