Set the oven to broil at 450°F. Place whole red peppers on a sheet pan and broil for 10-15 minutes, turning every 5 minutes with tongs until skins blister and char evenly. Transfer peppers to a bowl, cover tightly with plastic wrap, and let steam for 10 minutes to loosen skins.
Peel the charred skins off peppers under cool running water. Remove the stems and seeds, then pat the flesh dry with paper towels to remove excess moisture that could thin the dip.
Add peeled roasted peppers, crumbled feta cheese, Greek yogurt, and minced garlic to a food processor. Pulse 6-8 times until the mixture is slightly chunky, scraping down the sides once halfway through.
With the food processor running, slowly drizzle olive oil through the feed tube until the mixture turns creamy and smooth. Add lemon juice, smoked paprika, and a pinch of black pepper, then pulse twice more to combine.
Transfer the dip to a serving bowl, cover, and refrigerate for 30 minutes to thicken and meld flavors. Taste before serving and adjust salt carefully, as feta adds plenty of saltiness.
