Place a grill pan on the stove and warm over high heat (or, light a grill). Brush the quartered radicchio and sliced onions on all sides with olive oil and season with a sprinkle of salt and pepper.
When the grill pan is hot, place the radicchio and onion on the surface and “grill” for about 3-5 minutes per side for the radicchio, and 5-7 minutes per side for the onions, or until the vegetables are charred and tender when pierced with a fork. [If you are cooking on a real grill, you should probably use a grilling basket to prevent the vegetables from falling through the cracks]
Remove to a cutting board, let cool for a few minutes. Slice the radicchio crosswise into 1 1/2 inch slices, and cut each onion slice into thirds, separating the layers into individual pieces.
Meanwhile, place the baby spinach in a large salad bowl with the walnuts, blue cheese, parmesan, basil, and tomato. Add the warm grilled vegetables and toss to combine.
In a small bowl, whisk together the dressing ingredients (extra virgin olive oil, balsamic, garlic, Dijon mustard, and salt and pepper). Pour over the salad, toss to coat, and serve immediately. It goes great with crusty french bread and grilled shrimp as an easy summer supper.