3 tablespoons extra-virgin olive oil
1 1/2 pounds onions, peeled and cut into 1/2-inch wedges
8 tablespoons (1 stick) unsalted butter
4 pounds meaty cross-cut beef shanks (about 4 ossobuco)
1/2 teaspoon paprika
Fine sea salt
Freshly ground black pepper
3 (14.9-ounce) cans dark beer such as Guinness
2 cups low-salt or homemade beef broth
2 1/4 pounds Yukon gold potatoes
In a 5 1/2-quart Dutch oven or wide heavy pot with lid, heat oil over medium-high heat; add onions and cook, stirring frequently, until softened and golden, about 8 minutes. Remove pot from heat.
In a large heavy skillet, melt 2 1/2 tablespoons butter over medium-high heat. In batches, brown shanks, 3 to 4 minutes per side, wiping pan and adding up to 1/2 tablespoon more butter, if necessary.
Transfer shanks to a cutting board. Cut meat off bones (reserve bones); cut meat into 1-inch pieces. Transfer meat and bones to pot with onions; stir in paprika and season generously with salt and pepper. Add beer and 1 cup broth; bring to a simmer and cook, partially covered, adding remaining cup broth to pot as necessary to keep meat covered by at least 1 inch, until meat is very tender, about 2 hours.
When meat is 30 to 40 minutes from being done, put potatoes into a medium saucepan and cover with water by 2 inches. Bring water to a boil and cook until potatoes are tender, about 12 minutes or more, depending on size of potatoes. Drain and peel potatoes; transfer to a large bowl. Add remaining 5 tablespoons butter and coarsely mash; season to taste with salt and pepper. Cover to keep warm.
Using a slotted spoon, transfer meat, bones and onions to a large bowl. Into a second large bowl, strain braising liquid through a fine-mesh sieve; put any remaining onions into bowl with meat. Remove marrow from bones and stir into meat mixture; discard bones. Adjust seasoning.
Arrange meat and potatoes on a large serving platter; moisten with a little braising liquid. Serve warm.
Also made some cookies... 9 dozen!