In a large serving bowl, whisk together the lemon juice, honey, cinnamon and salt. Slowly stream in the olive oil while whisking. Set aside.
Slice the nectarine into 14-15 thin slices.
Heat a large 10” nonstick pan over medium heat. Add the butter.
When the butter melts, add the nectarine slices in one layer.
Let the nectarines cook on one side for 2 minutes, then flip.
After flipping the nectarines, gently tilt the pan, and using a spoon, spoon the butter over the nectarines to baste them. Cook for another 2 minutes and then remove the nectarines from the pan and let cool. Do not scrape out the pan.
Add the almonds to the pan and toast in the butter and nectarine juices.
Add the arugula to the bowl, followed by the peaches, almonds and cheddar chunks. Toss and serve.