dp <- getOption("default.datadir")  ## somehow set a file path to the file
f <- file.path(dp, "data/eclipse.ncdc.noaa.gov/pub/OI-daily-v2/NetCDF/1981/AVHRR/avhrr-only-v2.19810901.nc")

library(raster)
## Loading required package: sp
r <- raster(f)
## Loading required namespace: ncdf4
## Warning in .varName(nc, varname, warn = warn): varname used is: sst
## If that is not correct, you can set it to one of: sst, anom, err, ice
p1 <- "+proj=laea +lon_0=147 +lat_0=-42 +datum=WGS84"
ex1 <- extent(120, 160, -50, -30)

## it's not in-memory
basename(filename(r))
## [1] "avhrr-only-v2.19810901.nc"
proj1 <- projectRaster(r, 
                       projectExtent(raster(ex1, res = 0.25, crs = projection(r)), p1))

plot(proj1)

p2 <- "+proj=stere +lat_0=90  +datum=WGS84"
ex2 <- extent(-180, 180, 30, 90)

## remember to rotate this 0,360 raster

r180 <- rotate(r)
proj2 <- projectRaster(r180, projectExtent(crop(r180, ex2), crs = p2))
plot(proj2)

## BA BOM
#proj2 <- projectRaster(crop(r, ex2), crs = p2)
#Error in if (value[1] != nrow(x) | value[2] != ncol(x)) { : 
#    missing value where TRUE/FALSE needed
#  In addition: Warning message:
#    In `dim<-`(`*tmp*`, value = c(nr, nc)) :
#    NAs introduced by coercion to integer range