1. Rinse pork and pat dry; trim off any excess fat. Cut each chop in half horizontally to make a total of eight thin pieces. Working with two at a time, sandwich pieces between sheets of plastic wrap. Using a rolling pin or the flat side of a meat mallet, pound pork to an even 1/4 in. thick and season on both sides with salt and pepper. Pour flour into a wide, shallow bowl. Dip each piece of pork in flour, turning to coat completely. Discard remaining flour.
2. In a medium frying pan over medium heat, combine 2 tbsp. olive oil with 1 tbsp. butter. When melted and hot, add shallots and cook, turning occasionally, until lightly browned, about 5 minutes. Reduce heat to medium-low and add vinegar and sugar. Cook, stirring occasionally, until shallots are well browned and soft when pierced, about 20 minutes.
3. About 5 minutes before shallots are done, in a large frying pan over medium-high heat, combine remaining 2 tbsp. olive oil and 1 tbsp. butter. When melted and hot, add pork in a single layer (in batches if necessary) and cook, turning once, just until lightly browned on both sides and no longer pink in the center (cut to test), about 4 minutes total per batch.
4. Transfer pork to a warm platter and cover with foil. Add chicken broth and wine to pan and stir to scrape up any browned bits. Boil until liquid is reduced by a quarter, about 2 minutes. Season to taste with salt and pepper, then add shallots to pan. Mix to coat, then pour around pork.
Wine note: Riesling is one of the world's great white grapes. But early versions from the West tended to be simple, syrupy sweet, and flabby, and its reputation as schlock was sealed. The truth is, Riesling comes in a range of sugar levels, from bone dry to quite sweet. Those from Alsace, France, lean toward very dry; German bottles run the gamut. But the best have great acidity that keeps the wine crisp and refreshing, no matter how sweet. And stone fruit, apple, pear, and citrus flavors often come along with hints of flowers, minerals, and what can only be described as a haunting diesel-fuel quality--if you can imagine that as a good thing.
It's that acidity that makes Riesling a great food wine: Drier ones are wonderful with shellfish (the fruit picks up on the sweetness of crab and shrimp), sushi, poultry, pork, salty cured meats like ham, and--surprisingly--eggs; sweeter versions do well with sweet-and-sour dishes and spicy Thai or Southwestern food.
Claiborne & Churchill Dry Riesling 2005 (Central Coast; $18). Alsatian-style--dry, minerally, with crisp peaches and citrus; try it with the pork.
Mandolin Riesling 2004 (Monterey; $10). Quite dry, with crisp peaches and acid; great with the pork.
Note: Nutritional analysis is per serving.