Step 1

Heat oil in a large skillet over high. Cook beef, breaking up with a spoon, until browned on all sides but not completely cooked through, 6–8 minutes. Transfer to a medium bowl, leaving as much fat in pan as possible.

Step 2

Reduce heat to medium and cook onion, bell pepper, and garlic, stirring, until tender but not browned, 6–8 minutes; season with salt and pepper. Add cumin and chili powder and cook, stirring, until fragrant, about 1 minute. Add chicken stock and reserved beef along with any accumulated juices to pan. Bring to a simmer and cook, stirring and scraping up any brown bits from the skillet, until liquid is evaporated, 8–10 minutes; season with salt and pepper. Transfer to a medium bowl, cover, let sit until ready to use.

Step 3

Do Ahead: Picadillo can be made 1 day ahead. Cover and chill. Reheat before assembling.

Step 4

Melt butter in a medium saucepan over medium heat. Cook onion, chile, jalapeños, and garlic, stirring, until tender but not browned, 8–10 minutes. Add tomatoes, season with salt, and continue to cook until juices have evaporated, about 6 minutes. Stir in flour and cook until incorporated, about 1 minute. Whisk in milk and continue to cook until mixture comes to a boil and thickens, about 4 minutes. Reduce heat to low, gradually add both cheeses, and cook, stirring constantly, until cheese is completely melted and queso is smooth. If it seems too thick, stir in a little more milk.

Step 5

Spread warm picadillo in a 2-qt. baking dish. Pour hot queso over meat. Top with a generous scoop each of pico de gallo, guacamole, and sour cream. Sprinkle with chives and cilantro. Serve hot dip with chips.

Step 6

Do Ahead: Queso can be made 1 day ahead. Cover and chill. Reheat before assembling.