Step 1

Bring milk and 1 cup water to a boil over medium-high heat. Whisking constantly, gradually add grits and cook, turning down heat to maintain a low simmer if needed, until tender, 25–35 minutes. Whisk in cheese and butter to melt; season grits with salt and pepper.

Step 2

While grits are going, combine scallions, jalapeño, and oil in a small saucepan and bring to a simmer over medium heat, swirling pan occasionally, until scallions are lightly browned and crisp, 8–10 minutes. Using tongs, transfer scallions and jalapeño to a plate. Strain oil through a fine-mesh sieve into a small bowl.

Step 3

Divide grits among bowls. Top each with an egg and some scallions and jalapeño; drizzle with strained oil.