Preheat the oven to 350°F. Line 2 baking sheets with parchment paper.
In a medium bowl, whisk together the flour, ginger, nutmeg, baking soda, and salt. Set aside.
In a large bowl, use a hand mixer to cream together the sugar, molasses, vegetable oil, molasses, oat milk, and vanilla extract.
Gradually beat in the flour mixture until it forms a stiff and sticky dough.
Lightly wet your hands and roll the dough into approximately 24 balls, placing them on the cookie sheets about 3 inches apart.
Bake for 12 minutes, until the edges begin to brown. Remove from the oven and let the cookies rest on the cookie sheets for 5 minutes. Transfer to wire racks to cool completely.