Dissolve a portion of the salt into four cups of water in a large bowl, add the lentils, and soak for 1 hour at room temperature. This softens the skins to ensure they don't burst during the bake.

Adjust an oven rack to the middle position and heat the oven to 325°F. Drain and rinse the lentils well.

Combine the soaked lentils, the remaining four cups of water, salt, garlic, and bay leaf in an ovenproof medium saucepan. Bring the mixture to a boil over high heat on the stove.

Cover the pan tightly with a lid and transfer it to the oven. Bake until the lentils are tender but still hold their shape, about 30 to 50 minutes.

Whisk the olive oil and white wine vinegar together in a large bowl while the lentils finish cooking.

Drain the lentils through a fine-mesh strainer and discard the garlic and bay leaf. Add the warm lentils to the dressing and toss gently to coat, then let the mixture rest for 5 minutes to absorb the flavors.

Fold in the olives, mint, and shallot. Season with salt and pepper to taste, then sprinkle with feta and serve warm or at room temperature.