Plain ol' grilled cheese is kids' stuff.
In a large nonstick skillet, heat 1 tbsp. oil over medium. Add the Brussels sprouts and shallot; season with salt and pepper. Cook, stirring occasionally, until tender, about 8 minutes. Transfer to a bowl. Wipe out the skillet.
Brush 1 side of each slice of bread with oil. Sprinkle with the Parmesan, pressing gently so the cheese adheres to the bread. Turn the slices over and spread with 2 tbsp. Dijon. Layer 4 slices with half the fontina, the Brussels sprouts and shallot, and the remaining fontina. Top with the remaining slices of bread, cheese-side up. In the same skillet, heat 1 tbsp. oil over medium. Cook the sandwiches until toasted, 3 to 4 minutes per side.
In a large bowl, whisk the remaining 2 tbsp. olive oil, the vinegar, and the remaining 1/2 tsp. Dijon; season the dressing. Add the kale, apple, and almonds; season. Toss until coated. Serve the salad with the sandwiches.