Warm 1 Tbsp. oil in a large saucepan over medium-high heat. Add shallot and cook, stirring, until softened, about 3 minutes. Add peas, broth and 1 cup water and bring to a boil over high heat. Reduce heat to medium and cook until peas are very soft, about 5 minutes. Remove from heat and let cool slightly, about 5 minutes. Working in batches if necessary, puree soup in a blender and return to saucepan. Stir in half-and-half and season generously with salt and pepper. Keep warm over medium-low heat.
Warm remaining oil in a large nonstick skillet over high heat until hot. Sauté ham in batches until browned and curled around the edges, turning once, about 1 minute total. Transfer to a paper towel-lined plate to drain.
Ladle soup into bowls. Tear ham into bite-size pieces and add some to each bowl. Scatter croutons over soup and serve immediately.