Bring plums and 3/4 cup water to a boil in a small saucepan. Reduce heat to medium-high and simmer, stirring occasionally and mashing the plums with the back of a spoon, until plums have completely broken down, about 15 minutes.
Pour plum mixture through a fine-mesh sieve set over a small bowl, pressing on the solids to extract as much puree as possible; discard solids in sieve. Let puree cool.
Add oil, vinegar, and 2 tablespoons water to the puree; whisk to blend. Season dressing to taste with salt and pepper. (Dressing can be made 1 week ahead. Cover and chill)
Divide the greens among plates. Scatter nectarines, cheese, and almonds over, dividing equally, and drizzle some of the dressing over. Season with salt and pepper.