Caramelize the Onions
Rim the tip and root from the onions, cut them in half and remove the skins.
Slice the onion from root to stem into thin slices.
Heat 2 Tbsp olive oil, in your largest skillet over high heat.
When hot, stir in the onions along with a few pinches of salt. Cook for a few minutes, stirring often, until the onions soften up - 4-5 minutes.
Turn the heat down to medium and stir in the butter.
Turn the heat down to medium and stir in the butter. Stirring regularly, cook another 10 - 15 minutes at this temperature, or until the onions just begin to caramelize a bit.
Dial the heat back a shade more, and cook until the onions are deeply golden (this might take another 20 minutes or so)
Remove the pan from the heat and set aside the onions
Heat oil in a small saucepan over medium heat.
Cook the onion, stirring occasionally, until beginning to brown (~ 5–8 minutes)
Add the ketchup, dates, and beer. Bring to a boil, and then reduce the heat, and simmer, stirring occasionally (add water if you need, to prevent burning), until thick and slightly darkened (~ 20–25 minutes)
Remove pan from heat and stir in vinegar. Let cool slightly.
Purée in a food processor, thinning with water if needed, until smooth; season with salt and pepper. Let cool.
Sliders and assembly
Using your hands, gently mix onion, garlic, lamb, beef, parsley, and baharat in a large bowl.
Season with salt and pepper.
Form scant 1/4-cupfuls of lamb mixture into twelve 2"-diameter patties.
Heat oil in a large skillet over medium-high heat. Place patties in skillet and immediately reduce heat to medium. Cook about 3 minutes per side for medium-rare.
Serve patties on buns with date ketchup, arugula, caramelized onions, and feta.