Heat a grill pan over high. Preheat the oven to 375 degrees. Brush the bread with 3 tbsp. oil; season with salt and pepper. Grill 5 minutes per side. Tear into large pieces; place in a large bowl.
In a large skillet, cook the sausage over medium-high, breaking up with a spoon, until browned, about 8 minutes; add to the bread. In the skillet, heat 1 tbsp. oil over medium-high; add the onion. Cook, stirring often, until starting to soften, about 3 minutes. Add the apple and rosemary. Cook, stirring often, until the apple softens, about 2 minutes. Add the kale; stir until wilted, 2 to 3 minutes. Add to the bread; season.
In a medium bowl, whisk 2 cups stock and the eggs. Toss with the bread, adding more stock by the tablespoon if dry. Transfer to a 3-qt. baking dish.
Bake until a tester inserted into the center comes out clean, about 45 minutes. Let cool 10 minutes.