In a large skillet, heat the oil over medium heat. Add the onion and cook, stirring, until softened, about 5 minutes. Add the garlic, salt, allspice, ginger, and nutmeg and cook for 1 minute, until fragrant.
Transfer the onion mixture to a large bowl. Reserve the skillet for the gravy (no need to rinse).
Add the panko, egg, milk, and parsley to the bowl with the onions, and stir to combine. Add the beef and turkey and with your hands, mix until just combined; do not over-mix, or the meat will become tough.
Shape the mixture into 12 1½-inch meatballs and place on a baking sheet or large plate. Cover with plastic wrap and refrigerate for at least 15 minutes or up to overnight.
Place a rack in the top third of your oven and preheat to 425°F. If necessary, arrange the meatballs on a baking sheet. Bake on the top rack for 20 minutes, until nicely browned and cooked through. Switch the oven to broil and broil for 2-3 minutes, until golden brown on top. Watch carefully as they broil to avoid burning.
While the meatballs cook, make the gravy: Combine the broth, Worcestershire sauce, and mustard in a liquid measuring cup. Place the sour cream in a small bowl.
Melt the butter in the reserved skillet over medium heat. Add the flour and cook, stirring constantly, until light brown, about 2 minutes. Slowly add the broth mixture, whisking constantly to prevent lumps from forming, until fully combined. Bring to a simmer, stirring, until thickened.
Transfer about ¼ of the gravy mixture to the bowl with the sour cream and stir to combine (this tempers the sour cream so it doesn't separate in the hot gravy). Add the sour cream mixture to the rest of the gravy in the skillet and stir to combine. Turn off the heat.
Once the meatballs are cooked, transfer them to the skillet with the gravy and stir to combine. Garnish with fresh parsley and serve.
Notes
TO STORE: Leftover Swedish meatballs can be stored in an airtight container in the refrigerator for up to 3 days.
TO REHEAT: Heat the meatballs and gravy together in a skillet over medium heat until warmed through, or use the microwave.
TO FREEZE: You can freeze Swedish meatballs and gravy in a freezer-safe container or bag for up to 3 months. Thaw in the refrigerator before reheating according to the instructions above.