Preheat oven to 325°F. Season ribs well on all sides with salt and pepper. Put the flour into a pie plate, season with salt and pepper, and mix well. Dredge the ribs in the flour, coating completely and shaking off the excess. Heat the oil in a large Dutch oven (large enough to hold the ribs lying down) over medium-high heat. Sear the ribs until golden brown on all sides. Transfer to a plate.
Add onions, bay leaf, paprika and crushed caraway seeds to the pot. Season with salt and pepper, and cook, stirring frequently, until the onions are beginning to turn golden, 12-15 minutes. Add the tomatoes and stir until well-combined.
Set the ribs on top of the onions, rounded sides down, and pour in any accumulated juices from the plate. Bring to a simmer, cover, and transfer to the oven. Cook, turning the ribs over halfway through the cooking time, until the meat is very tender and falling from the bones, 2 to 2 1/2 hours. Remove the ribs from the pot and cover to keep warm.
Taste the goulash and season with salt and pepper if necessary. Stir in the balsamic vinegar. To serve, divide the goulash among four shallow bowls and set a rib on top of each serving. Garnish with a sprinkling of toasted caraway seeds, paprika, and chopped parsley, if using. Serve immediately, with mashed potatoes.
****Notes for using pressure cooker: After the ribs are seared with the onions, etc., everything goes into the pressure cooker and cooks for 25 minutes (so it’s a 30-minute total cook time vs 2.5 hours).