In a medium bowl, stir together pimientos, mayonnaise, cream cheese, mustard, and ½ teaspoon salt. Fold in Cheddar. Cover and refrigerate until ready to use.
Heat a cast-iron grill pan over medium heat until slightly smoking. Lightly spray pan with cooking spray.
Lightly brush cut sides of peaches and avocados with olive oil. Place peaches, cut side down, on prepared pan. Cook until peaches are just soft and charred, 3 to 4 minutes. Remove and set aside. Place avocados, cut side down, on pan. Cook until just soft and charred, 2 to 3 minutes. Remove and set aside. Brush both sides of each bread slice with olive oil. Place bread on pan. Cook until toasted and charred, 5 to 6 minutes, turning once halfway through. Let cool completely on a wire rack.
Scoop avocado pulp into a small bowl. Add lime juice, remaining ⅛ teaspoon salt, and pepper. Using a fork, mash avocado until mostly smooth. Set aside. On a flat working surface, slice peaches ⅛-inch thick.
To assemble, place toasts on a serving platter. Spread desired amount of cheese mixture onto toasts. Divide avocado mixture evenly between toasts atop cheese mixture. Equally divide sliced peaches among toasts, slightly overlapping peaches to create a shingled effect. Garnish with radish sprouts, if desired. Serve immediately.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/pimiento-cheese-and-grilled-peach-toast/