Grill sausages over medium-high heat until cooked through, reserve.
While sausages are grilling, combine the rosemary and mayonnaise, reserve.
Heat a skillet over medium-high heat, add the oil, and sauté the garlic until just beginning to brown.
Add the spinach and cook until water has evaporated, reserve.
Warm the slider rolls on the grill, taking care not to burn them.
To assemble, dress the top of each roll with a generous amount of the mayonnaise, slice the sausages on a bias, and place 1/3 of a link on the bottoms of each of the rolls. Top with spinach, then the cheese, then top with the dressed rolls.