Put all of the ingredients for the sauce in food processor and process until smooth. Transfer to a small serving dish and reserve.
Put the red onion rings in a small bowl and separate the rings. Add the lime juice and drizzle with extra-virgin olive oil. Season with salt and pepper, to taste.
Add the lamb to a mixing bowl along with the garlic, chile, ginger, spices, cinnamon, and salt and pepper, to taste. Mix to combine. Form the meat mixture into 4 sections and make 2 slider-size patties form each portion, 8 (3-ounce) burgers in total, thinner at the center and thicker at the edges.
Heat a large skillet or a griddle pan with a drizzle of extra-virgin olive oil over medium-high heat. Add the burgers and cook a few minutes on each side.
Put a few leaves of spinach on each of the bun bottoms and add the burger. Top with the onions and green sauce. Cover with the bun tops and serve.
* Toast and grind your own coriander and cumin if you have a coffee grinder or spice mill.