Stir or toss walnuts in a dry pan over medium heat until very hot to the touch and toasted, about 5 minutes.
Mix Dijon mustard, rice vinegar, balsamic vinegar, and pepper together in a bowl for dressing. Pour in olive oil, about 1 teaspoon at a time, whisking constantly, until thick and coats the back of a spoon. Taste and adjust as necessary.
Cut radicchio in half; cut out the core using 2 angled cuts. Cut each half in half again and slice across into about 1-inch pieces. Slice root ends off of endive and peel off about 1/3 of the leaves, leaving them whole for presentation. Slice remaining endive into 1/2-inch pieces.
Transfer all radicchio and endive to a bowl and toss, making sure leaves are separated and evenly distributed. Crumble in about 1/2 of the walnuts and 1/2 of the blue cheese. Pour in dressing and toss with your hands until everything is perfectly coated.
Place whole endive spears on a serving plate. Pile salad on top and scatter remaining walnuts and blue cheese on top.