Arrange a rack in upper third of oven; preheat to 400°. Place tomatoes on a small foil-lined baking sheet.

Roast tomatoes until softened and blistered, about 30 minutes. Transfer to a wire rack and let cool slightly.

In a blender, pulse tomatoes, onion, garlic, parsley, salt, and chili powder until smooth. Transfer to a medium bowl; set aside until ready to use.

In a medium skillet over medium-high heat, heat oil. Cook onion and garlic, stirring occasionally, until onion is lightly golden and translucent, about 5 minutes.

Stir in beans, salt, and cumin. Cook, stirring occasionally, until warmed through, about 5 minutes. Using the back of a fork, mash beans; set aside until ready to use.

In a large bowl, combine masa, water, and salt. Using your hands, shape dough into a ball.

Divide dough into 6 (2.5-oz.) pieces. Using a tortilla press or a flat plate, pie dish, or skillet, flatten dough into ½"-thick rounds 3 ½" to 4" in diameter.

In a medium cast-iron skillet or comal over medium-high heat, cook 2 rounds at a time, turning once, until barely golden and still pliable, 1 to 2 minutes per side; a light skin will form and begin to look like a tortilla. Transfer to a cutting board and let cool slightly. Using your pointer fingers and thumbs, form a ¼"- to ½"-high border around sope. Repeat with remaining dough.

In same skillet or comal over medium heat, heat oil until an instant-read thermometer registers 325°. Cook 3 sopes at a time, turning once, until lightly golden brown, 1 to 2 minutes per side.

Build sopes with chicken, lettuce, onion, cotija, crema, radishes, beans, and salsa.