Do you remember the widely used DS3231 RTC Module ?As you might rememeber we have identified onboard an EEPROM chip, a 32k AT24C32 one and have written some driver examples for LUA
I was looking a few days ago for a I2C EEPROM to do some tests with ESPBasic and the results…can be seen below 
1. MAIN Program
cls i2c.setup(4,5) 'choose your I2C bus pins let eeprom_address = 0 'EEPROM memory start address i2c_address = 87 ' 0x57 - AT24C32 I2C address let i = 0 stw = "87654321" 'string that we want to save in EEPROM button "i2c Read",[I2C_read] button "i2c Write",[I2C_Write] wait
2. EEPROM READ Function
[I2C_read] stwl = len(stw) print "Reading from I2C address " & i2c_address adrh = eeprom_address >> 8 adrl = eeprom_address and 255 i2c.begin(i2c_address) i2c.write(adrh) i2c.write(adrl) i2c.end() i2c.begin(i2c_address) i2c.requestfrom(i2c_address,stwl) tr = i2c.available() print "Available bytes :" & tr do i2c_read = i2c.read() readt = i2c_read-48 print "Read value : " & readt i = i + 1 loop while i < tr i = 0 i2c.end() print "Read complete" wait
3. EEPPROM WRITE function
[I2C_Write] print "Writing to I2C address " & i2c_address stwl = len(stw) print "String : " & stw print "String Lenght : " & stwl adrh = eeprom_address >> 8 adrl = eeprom_address and 255 i2c.begin(i2c_address) i2c.write(adrh) i2c.write(adrl) i = 1 do stru = mid(stw,i,1) print "Value to Write: " & asc(stru) i2c.write(asc(stru)) i = i + 1 loop while i < stwl+1 i = 0 i2c.end() print "Write complete" wait
Of course, this is just a proof of concept driver example for the I2C 24C32 EEPROM but I think might help you with a good start
Happy breadboarding,
TJ.
