Preheat oven to 400 degrees and line a baking sheet with parchment. Mix hot water, honey, rosemary, and salt in a small bowl until honey dissolves. Creating a simple syrup out of the honey makes it much easier to apply to the squashes. Lay squashes on the baking sheet and first brush with olive oil, then the rosemary honey until well coated. Reserve some honey for later, maybe a tablespoon or two. Roast squashes for 50-60 minutes until fork-tender.
In the last 30 minutes of the squashes' cooking time, start preparing the barley-mushroom mixture. Heat 1 tbsp olive oil over medium. Add shallots and garlic and cook until shallots soften and mixture is fragrant, about 1-2 minutes. Add mushrooms, rosemary, and a touch of salt and pepper. Stir once, then let simmer, undisturbed, for 3 minutes before tossing again. Repeat the sit-stir process two or three more times until mushrooms release some of their juices and are caramelized around the edges. Toss in barley and toast for 2-3 minutes, then add broth or water. Bring to a boil, then reduce heat to a simmer and cook for 15-20 minutes until barley absorbs most of the water and is tender but chewy. Turn off heat and add kale. Stir until wilted, about a minute or two.
By the time your filling is ready, the squashes should be cooked. If the timer went off in the process of concocting the barley blend, be sure to remove the squashes from the oven and set aside.
When all components are complete, turn the broiler to HIGH. Spoon the barley mixture evenly between the acorn squash halves. Top with feta cheese. Drizzle remaining rosemary honey over each squash. Place under the broiler for 3-4 minutes until feta bubbles and turns a nice golden brown. Be careful not to burn! Serve warm with chopped parsley, if desired.