'The Unique' was recorded in the spring of 1956 and 'Brilliant Corners' in the fall. I think this year marks a real breakthrough for Monk - I've been listening to the discography in chronological order, and I feel like this would be a good place for a transition from an 'early' period to 'middle' period for Monk.
He's here with Art Blakey on drums and Oscar Pettiford on bass, and it's all Monk, and he is masterful. It starts with a jaunty 'Liza, All The Clouds Will Roll Away', moving into a meditative, thoughtful, 'Memories of You'. 'Honeysuckle Rose' starts out peppy, almost old-timey, like if you transported Monk back to the 1930's for a minute, and then it just rolls. He's almost solo on 'Darn That Dream' and 'Tea for Two', where Pettiford does some nice bass work. Monk is all up and down the scales on 'You Are Too Beautiful', and he ends with 'Just You, Just Me', where he plays the piano like it was a set of drums.
Obviously, I can't pick a favorite here. Throw in the iconic postage stamp album art, and this is the earliest Monk album I can definitely describe as 'must have' for any jazz enthusiast.