In a michael reaction, an a carbon attacks the b carbon of an a, b-unsaturated carbonyl compound to afford a 1,5-dicarbonyl compound. ethyl acetoacetate has two a carbons: why does the a carbon sandwiched between the two carbonyls conduct the attack?

Explanation:

The middle carbon which is  in between  the two carbonyl groups. One of the carbonyl group is a ketone whereas the other carbonyl group is of an ester.

Since both the carbonyl groups are appreciably electron-withdrawing  and hence they withdraw the electron density from the central carbon atom  to quite a extent and hence making the hydrogens quite acidic.

Also the carbanion generated on the central carbon atom after the proton abstraction can be appreciably stabilized by conjugation on the two carbonyl groups. Due to this stabilization the carbanion happens to be stable and attacks the b position of   of  a,b unsaturated carbonyl compound .

Kindly refer the attchment for the reaction and structure.

Michael addition is a reaction of stabilized enolate which reacts to give a conjugate addition.