In a Dutch oven, combine pork cubes with ½ cup water and ½ tsp salt over medium heat. Cover and cook 20 minutes, stirring occasionally.

Uncover, raise heat to medium-high, and continue cooking until liquid evaporates and pork browns in its own fat (another 15–20 min). Transfer pork to a bowl and set aside.

Preheat broiler with racks positioned: one 6 inches below element, one low. Line a foiled baking sheet with spray. Arrange Anaheim chiles, skin side up, and jalapeños in a single layer. Broil 15–20 minutes, rotating sheet and flipping jalapeños halfway, until skins are blistered.

Place Anaheims in a bowl and cover with plastic wrap to steam. Let cool ~5 minutes.

Skin Anaheims, then chop half into ½‑inch pieces. Purée the other half until smooth. Pulse tomatoes with juice in food processor until coarsely ground.

In the same Dutch oven, heat oil over medium heat. Add onions and cook 5–7 minutes until lightly browned. Stir in garlic and cumin and cook ~30 seconds until fragrant.

Add flour, stir and cook 1 minute (to remove raw flavor). Then add chicken broth, puréed and chopped Anaheims, tomatoes, and reserved pork (with their juices). Scrape up browned bits. Bring to simmer. Cover, move to lower oven rack, and braise until pork is tender, 1–1¼ hours.

Stem, seed, and finely chop jalapeños. Stir into chili. Season with salt, cayenne, and any reserved jalapeño seeds to your heat preference.

Serve hot with lime wedges.