Preheat grill or oven to 350 degrees F (180 degrees C). If using grill, turn on side burners only, cooking peaches in the center over indirect heat.
Using a food processor, blend Almonds (1/3 cup), Brown Sugar (1/4 cup), Ground Cinnamon (1/4 teaspoon), Ground Ginger (1/8 teaspoon), and Salt (1 pinch) until a course crumb is achieved.
Add Oatmeal (1/4 cup) and pulse several times to combine. Add Butter (3 tablespoon) and pulse until mixture is evenly mixed and crumbly.
Lay Peach (4) cut side up in a cast iron skillet, trimming bottom slightly if needed to make peaches sit flat. Scoop 3 tablespoons of lightly packed crumb mixture onto each peach half. Press down mixture until flat and covering entire peach half.
Place in center of grill using indirect heat or place in oven and cook for 40-50 minutes, until peaches are tender and crumble is golden and crisp.
Serve warm, topped with whipped cream if desired.