Heat a large skillet over medium heat with 2 Tbsp of olive oil. Dice the onion and add it to the skillet along with the minced garlic. Cook over medium heat until the onions are soft and translucent (5-10 minutes).
Once the onions are translucent, add the roasted tomatoes, tomato paste, and diced green chiles. Also stir in 1/2 cup of water, 3/4 tsp of salt, and 1/2 tsp of cumin. Stir everything together and allow it to come up to a simmer over medium heat.
Make four indentations in the sauce with the back of a large spoon. Crack an egg into each. Reduce the heat to low, place a lid on top of the skillet and allow the mixture to simmer while you make the grits. It should take about 10 minutes of simmering on low with a lid for the eggs to poach.
In a medium pot with a lid, bring 3 cups of water to a boil over high heat. Once it reaches a rolling boil, stir in the 3/4 cup of quick cooking grits and 3/4 tsp salt. Reduce the heat to low, place a lid on the pot, and allow it to cook on the lowest heat setting for 5 minutes. After five minutes it should be thick. Turn off the heat and stir in the butter. Place the lid back on the pot to keep them warm until you’re ready to serve.
Once the eggs are done cooking, spoon some grits into a bowl and top with an egg and a spoonful or two of the tomato sauce. Add sliced fresh green onions on top.