Preheat the oven to 400°F. Heat the olive oil in a large cast-iron (or other oven-safe) sauté pan over medium heat.
When the oil is hot, add the onion and sauté until tender, 4 to 5 minutes. Add the garlic and jalapeños and cook until fragrant, 1 minute more.
Add the ground beef, and cook until it’s well browned, 6 to 7 minutes. Stir in the taco seasoning, and season with salt and pepper. Add the salsa and tomatoes and bring to a simmer. Simmer for 2 to 3 minutes, stirring occasionally.
Remove the pan from the heat and then add both cheeses in an even layer. Bake until the cheese is melted and the chili is bubbly, 8 to 10 minutes.
Let cool 5 to 10 minutes before serving warm, garnished with green onions. Serve with tortilla chips.