Answer:
The organizational pattern Elizabeth Browning's sonnets follow is the Italian (Petrarchan) one.
Explanation:
Petrarchan sonnet is a type of poem consisting of 14 lines divided into two stanzas, one with eight and the other with 6 lines. The rhyme scheme for the first stanza is ABBAABBA, while for the second one it is CDCDCD or CDECDE. Elizabeth Browning chose this type of sonnet to write. Let's take a look at one of her most famous sonnets:
How do I love thee? Let me count the ways.  A
I love thee to the depth and breadth and height  B
My soul can reach, when feeling out of sight  B
For the ends of being and ideal grace.  A
I love thee to the level of every day’s  A
Most quiet need, by sun and candle-light.  B
I love thee freely, as men strive for right;  B
I love thee purely, as they turn from praise.  A
I love thee with the passion put to use  C
In my old griefs, and with my childhood’s faith.  D
I love thee with a love I seemed to lose  C
With my lost saints. I love thee with the breath,  D
Smiles, tears, of all my life; and, if God choose,  C
I shall but love thee better after death. D