Preheat the oven to 400°F (200°C).
Trim the top off the garlic bulb to expose the cloves, drizzle with about 1 teaspoon olive oil, wrap in foil, and place on a baking sheet.
Brush the jalapeños with the remaining 1 tablespoon olive oil and season lightly with salt and pepper; place them on the baking sheet alongside the garlic.
Roast the garlic and jalapeños in the oven for 25–30 minutes, until the garlic is golden and the jalapeños are charred; remove and let cool until safe to handle.
When cooled, peel the jalapeños, halve and discard the stems and seeds, then finely chop the peppers. Use caution to avoid touching your eyes.
Squeeze the roasted garlic cloves out of the bulb into a large bowl.
Crumble both 8-ounce feta bricks into the bowl with the roasted garlic.
Add the chopped jalapeños, lemon zest and lemon juice from half a lemon, and 1/4 cup olive oil to the feta.
Mash everything together with a fork until you reach a spreadable, slightly wet consistency—adjust by mashing more or adding a touch more oil if desired.
Taste and season with salt and pepper as needed, then serve with pita, chips, or bread.