Heat olive oil in a large skillet over high heat. Add the squash and sprinkle with dry spices. Cook for several mins, turning gently with a spatula, until the squash is deep golden brown and tender (but not falling apart). Remove and set aside.
In the same skillet, add more olive oil over medium-high heat and add in the kale. Toss it around with tongs and cook it for 3-4 mins. Add in the cooked squash and gently toss together.
Build the quesadillas starting with a tortilla, adding a layer of the goat cheese on the bottom and a layer of the squash/kale mixture and top with the Monterey Jack and a second tortilla.
Grill in a panini press until cheese is nicely melted