Preheat oven to 425ºF. In a large bowl, toss squash slices with 2 tbsp of the olive oil, maple syrup, salt and allspice; spread in a single layer on a parchment-lined baking sheet. Bake 20-25 minutes, until squash is tender and starting to caramelize.
Meanwhile, arrange Halloumi slices in a single layer on a second baking sheet; brush with 1/2 tbsp olive oil.
Gently flip squash slices and return to oven, along with Halloumi; bake 5-10 minutes more, until Halloumi is soft and starting to brown at edges.