Heat 1 tablespoon neutral oil in large heavy skillet over medium-high heat. At the same time, place peppers in medium bowl with additional oil and toss to coat.
When skillet is hot, add peppers in one even layer. Work in batches if needed to avoid overcrowding the skillet. Sauté peppers uncovered.
Let peppers cook undisturbed, other than quickly stirring them approximately every 2 minutes. Sauté until blistered and charred, approximately 6 to 8 minutes total.
While peppers sauté, make lemon-garlic aioli. Add mayonnaise, garlic, salt, and juice of 1 quarter of lemon to bowl. Combine thoroughly. Taste and adjust salt and/or lemon juice as desired.
When peppers are blistered (softened and charred in spots), add 1 tablespoon butter to skillet and let melt. Squeeze juice of 1 quarter of lemon over peppers. Sprinkle with plenty of salt and use tongs to toss peppers to coat in butter and lemon juice.
Transfer peppers to plate, or serve in skillet, with lemon-garlic aioli.